[{"data":1,"prerenderedAt":5762},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Fnumerics\u002Fnewton-verfahren-gleichungssysteme":546,"formula-related-de\u002Fformulas\u002Fmath\u002Fnumerics\u002Fnewton-verfahren-gleichungssysteme":5750},[4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,173,174,175,176,177,178,179,180,181,182,183,184,185,186,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545],{"category":5},"algebra",{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":65},"arithmetic",{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":101},"calculus",{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":172},"differential-equations",{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":187},"discrete-math",{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":208},"functions",{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":247},"geometry",{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":312},"linear-algebra",{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":368},"multivariable-calculus",{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":391},"numerics",{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":412},"sequences-series",{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":441},"stochastics",{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":518},"trigonometry",{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"id":547,"title":548,"aliases":549,"body":554,"category":391,"checks":5669,"conditions":5710,"conditionsHtml":5711,"deprecated":5712,"description":5663,"extension":5713,"figure":5712,"figureCaption":5712,"figureHtml":5712,"formulaId":5714,"latex":5715,"latexHtml":5716,"level":5717,"meta":5718,"navigation":5719,"path":5720,"redirectFrom":5721,"related":5722,"seo":5727,"stem":5728,"subject":580,"summary":5729,"tags":5730,"variables":5735,"__hash__":5749},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Fnumerics\u002Fnewton-verfahren-gleichungssysteme.md","Newton-Verfahren für Gleichungssysteme",[550,551,552,553],"mehrdimensionales Newton-Verfahren","Newton-Verfahren mehrere Variablen","Newton-Raphson für Systeme","nichtlineares Gleichungssystem numerisch lösen",{"type":555,"value":556,"toc":5662},"minimark",[557,562,760,1135,1503,1972,1975,2307,2499,2503,2506,3123,3323,3618,4137,4801,5143,5357,5361],[558,559,561],"h2",{"id":560},"erklärung","Erklärung",[563,564,565,566,569,570,669,670,700,701,729,730,759],"p",{},"Das ",[567,568,548],"strong",{}," sucht eine Nullstelle von ",[571,572,575,616],"span",{"className":573},[574],"katex",[571,576,579],{"className":577},[578],"katex-mathml",[580,581,583],"math",{"xmlns":582},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[584,585,586,611],"semantics",{},[587,588,589,593,598,601,604,607],"mrow",{},[590,591,592],"mi",{},"F",[594,595,597],"mo",{"stretchy":596},"false","(",[590,599,600],{},"x",[594,602,603],{"stretchy":596},")",[594,605,606],{},"=",[608,609,610],"mn",{},"0",[612,613,615],"annotation",{"encoding":614},"application\u002Fx-tex","F(x) = 0",[571,617,621,659],{"className":618,"ariaHidden":620},[619],"katex-html","true",[571,622,625,630,636,640,643,647,652,656],{"className":623},[624],"base",[571,626],{"className":627,"style":629},[628],"strut","height:1em;vertical-align:-0.25em;",[571,631,592],{"className":632,"style":635},[633,634],"mord","mathnormal","margin-right:0.1389em;",[571,637,597],{"className":638},[639],"mopen",[571,641,600],{"className":642},[633,634],[571,644,603],{"className":645},[646],"mclose",[571,648],{"className":649,"style":651},[650],"mspace","margin-right:0.2778em;",[571,653,606],{"className":654},[655],"mrel",[571,657],{"className":658,"style":651},[650],[571,660,662,666],{"className":661},[624],[571,663],{"className":664,"style":665},[628],"height:0.6444em;",[571,667,610],{"className":668},[633]," mit ",[571,671,673,687],{"className":672},[574],[571,674,676],{"className":675},[578],[580,677,678],{"xmlns":582},[584,679,680,685],{},[587,681,682],{},[590,683,684],{},"n",[612,686,684],{"encoding":614},[571,688,690],{"className":689,"ariaHidden":620},[619],[571,691,693,697],{"className":692},[624],[571,694],{"className":695,"style":696},[628],"height:0.4306em;",[571,698,684],{"className":699},[633,634]," Gleichungen und ",[571,702,704,717],{"className":703},[574],[571,705,707],{"className":706},[578],[580,708,709],{"xmlns":582},[584,710,711,715],{},[587,712,713],{},[590,714,684],{},[612,716,684],{"encoding":614},[571,718,720],{"className":719,"ariaHidden":620},[619],[571,721,723,726],{"className":722},[624],[571,724],{"className":725,"style":696},[628],[571,727,684],{"className":728},[633,634]," Unbekannten. Wie im eindimensionalen Fall ersetzt man ",[571,731,733,746],{"className":732},[574],[571,734,736],{"className":735},[578],[580,737,738],{"xmlns":582},[584,739,740,744],{},[587,741,742],{},[590,743,592],{},[612,745,592],{"encoding":614},[571,747,749],{"className":748,"ariaHidden":620},[619],[571,750,752,756],{"className":751},[624],[571,753],{"className":754,"style":755},[628],"height:0.6833em;",[571,757,592],{"className":758,"style":635},[633,634]," in der Nähe der aktuellen Näherung durch seine Linearisierung",[571,761,764],{"className":762},[763],"katex-display",[571,765,767,864],{"className":766},[574],[571,768,770],{"className":769},[578],[580,771,773],{"xmlns":582,"display":772},"block",[584,774,775,861],{},[587,776,777,779,781,795,798,802,804,806,809,811,813,825,827,829,837,839,851,853,857,859],{},[590,778,592],{},[594,780,597],{"stretchy":596},[782,783,784,786],"msup",{},[590,785,600],{},[587,787,788,790,793],{},[594,789,597],{"stretchy":596},[590,791,792],{},"k",[594,794,603],{"stretchy":596},[594,796,797],{},"+",[590,799,801],{"mathvariant":800},"normal","Δ",[590,803,600],{},[594,805,603],{"stretchy":596},[594,807,808],{},"≈",[590,810,592],{},[594,812,597],{"stretchy":596},[782,814,815,817],{},[590,816,600],{},[587,818,819,821,823],{},[594,820,597],{"stretchy":596},[590,822,792],{},[594,824,603],{"stretchy":596},[594,826,603],{"stretchy":596},[594,828,797],{},[830,831,832,835],"msub",{},[590,833,834],{},"J",[590,836,592],{},[594,838,597],{"stretchy":596},[782,840,841,843],{},[590,842,600],{},[587,844,845,847,849],{},[594,846,597],{"stretchy":596},[590,848,792],{},[594,850,603],{"stretchy":596},[594,852,603],{"stretchy":596},[854,855,856],"mtext",{}," ",[590,858,801],{"mathvariant":800},[590,860,600],{},[612,862,863],{"encoding":614},"F(x^{(k)} + \\Delta x) \\approx F(x^{(k)}) + J_F(x^{(k)})\\,\\Delta x",[571,865,867,942,966,1028],{"className":866,"ariaHidden":620},[619],[571,868,870,874,877,880,931,935,939],{"className":869},[624],[571,871],{"className":872,"style":873},[628],"height:1.188em;vertical-align:-0.25em;",[571,875,592],{"className":876,"style":635},[633,634],[571,878,597],{"className":879},[639],[571,881,883,886],{"className":882},[633],[571,884,600],{"className":885},[633,634],[571,887,890],{"className":888},[889],"msupsub",[571,891,894],{"className":892},[893],"vlist-t",[571,895,898],{"className":896},[897],"vlist-r",[571,899,903],{"className":900,"style":902},[901],"vlist","height:0.938em;",[571,904,906,911],{"style":905},"top:-3.113em;margin-right:0.05em;",[571,907],{"className":908,"style":910},[909],"pstrut","height:2.7em;",[571,912,918],{"className":913},[914,915,916,917],"sizing","reset-size6","size3","mtight",[571,919,921,924,928],{"className":920},[633,917],[571,922,597],{"className":923},[639,917],[571,925,792],{"className":926,"style":927},[633,634,917],"margin-right:0.0315em;",[571,929,603],{"className":930},[646,917],[571,932],{"className":933,"style":934},[650],"margin-right:0.2222em;",[571,936,797],{"className":937},[938],"mbin",[571,940],{"className":941,"style":934},[650],[571,943,945,948,951,954,957,960,963],{"className":944},[624],[571,946],{"className":947,"style":629},[628],[571,949,801],{"className":950},[633],[571,952,600],{"className":953},[633,634],[571,955,603],{"className":956},[646],[571,958],{"className":959,"style":651},[650],[571,961,808],{"className":962},[655],[571,964],{"className":965,"style":651},[650],[571,967,969,972,975,978,1016,1019,1022,1025],{"className":968},[624],[571,970],{"className":971,"style":873},[628],[571,973,592],{"className":974,"style":635},[633,634],[571,976,597],{"className":977},[639],[571,979,981,984],{"className":980},[633],[571,982,600],{"className":983},[633,634],[571,985,987],{"className":986},[889],[571,988,990],{"className":989},[893],[571,991,993],{"className":992},[897],[571,994,996],{"className":995,"style":902},[901],[571,997,998,1001],{"style":905},[571,999],{"className":1000,"style":910},[909],[571,1002,1004],{"className":1003},[914,915,916,917],[571,1005,1007,1010,1013],{"className":1006},[633,917],[571,1008,597],{"className":1009},[639,917],[571,1011,792],{"className":1012,"style":927},[633,634,917],[571,1014,603],{"className":1015},[646,917],[571,1017,603],{"className":1018},[646],[571,1020],{"className":1021,"style":934},[650],[571,1023,797],{"className":1024},[938],[571,1026],{"className":1027,"style":934},[650],[571,1029,1031,1034,1081,1084,1122,1125,1129,1132],{"className":1030},[624],[571,1032],{"className":1033,"style":873},[628],[571,1035,1037,1041],{"className":1036},[633],[571,1038,834],{"className":1039,"style":1040},[633,634],"margin-right:0.0962em;",[571,1042,1044],{"className":1043},[889],[571,1045,1048,1072],{"className":1046},[893,1047],"vlist-t2",[571,1049,1051,1067],{"className":1050},[897],[571,1052,1055],{"className":1053,"style":1054},[901],"height:0.3283em;",[571,1056,1058,1061],{"style":1057},"top:-2.55em;margin-left:-0.0962em;margin-right:0.05em;",[571,1059],{"className":1060,"style":910},[909],[571,1062,1064],{"className":1063},[914,915,916,917],[571,1065,592],{"className":1066,"style":635},[633,634,917],[571,1068,1071],{"className":1069},[1070],"vlist-s","​",[571,1073,1075],{"className":1074},[897],[571,1076,1079],{"className":1077,"style":1078},[901],"height:0.15em;",[571,1080],{},[571,1082,597],{"className":1083},[639],[571,1085,1087,1090],{"className":1086},[633],[571,1088,600],{"className":1089},[633,634],[571,1091,1093],{"className":1092},[889],[571,1094,1096],{"className":1095},[893],[571,1097,1099],{"className":1098},[897],[571,1100,1102],{"className":1101,"style":902},[901],[571,1103,1104,1107],{"style":905},[571,1105],{"className":1106,"style":910},[909],[571,1108,1110],{"className":1109},[914,915,916,917],[571,1111,1113,1116,1119],{"className":1112},[633,917],[571,1114,597],{"className":1115},[639,917],[571,1117,792],{"className":1118,"style":927},[633,634,917],[571,1120,603],{"className":1121},[646,917],[571,1123,603],{"className":1124},[646],[571,1126],{"className":1127,"style":1128},[650],"margin-right:0.1667em;",[571,1130,801],{"className":1131},[633],[571,1133,600],{"className":1134},[633,634],[563,1136,1137,1138,1207,1208,1211,1212,1283,1284,1502],{},"und setzt sie null. Die Rolle von ",[571,1139,1141,1162],{"className":1140},[574],[571,1142,1144],{"className":1143},[578],[580,1145,1146],{"xmlns":582},[584,1147,1148,1159],{},[587,1149,1150],{},[782,1151,1152,1155],{},[590,1153,1154],{},"f",[594,1156,1158],{"mathvariant":800,"lspace":1157,"rspace":1157},"0em","′",[612,1160,1161],{"encoding":614},"f'",[571,1163,1165],{"className":1164,"ariaHidden":620},[619],[571,1166,1168,1172],{"className":1167},[624],[571,1169],{"className":1170,"style":1171},[628],"height:0.9463em;vertical-align:-0.1944em;",[571,1173,1175,1179],{"className":1174},[633],[571,1176,1154],{"className":1177,"style":1178},[633,634],"margin-right:0.1076em;",[571,1180,1182],{"className":1181},[889],[571,1183,1185],{"className":1184},[893],[571,1186,1188],{"className":1187},[897],[571,1189,1192],{"className":1190,"style":1191},[901],"height:0.7519em;",[571,1193,1195,1198],{"style":1194},"top:-3.063em;margin-right:0.05em;",[571,1196],{"className":1197,"style":910},[909],[571,1199,1201],{"className":1200},[914,915,916,917],[571,1202,1204],{"className":1203},[633,917],[571,1205,1158],{"className":1206},[633,917]," übernimmt die ",[567,1209,1210],{},"Jacobi-Matrix"," ",[571,1213,1215,1233],{"className":1214},[574],[571,1216,1218],{"className":1217},[578],[580,1219,1220],{"xmlns":582},[584,1221,1222,1230],{},[587,1223,1224],{},[830,1225,1226,1228],{},[590,1227,834],{},[590,1229,592],{},[612,1231,1232],{"encoding":614},"J_F",[571,1234,1236],{"className":1235,"ariaHidden":620},[619],[571,1237,1239,1243],{"className":1238},[624],[571,1240],{"className":1241,"style":1242},[628],"height:0.8333em;vertical-align:-0.15em;",[571,1244,1246,1249],{"className":1245},[633],[571,1247,834],{"className":1248,"style":1040},[633,634],[571,1250,1252],{"className":1251},[889],[571,1253,1255,1275],{"className":1254},[893,1047],[571,1256,1258,1272],{"className":1257},[897],[571,1259,1261],{"className":1260,"style":1054},[901],[571,1262,1263,1266],{"style":1057},[571,1264],{"className":1265,"style":910},[909],[571,1267,1269],{"className":1268},[914,915,916,917],[571,1270,592],{"className":1271,"style":635},[633,634,917],[571,1273,1071],{"className":1274},[1070],[571,1276,1278],{"className":1277},[897],[571,1279,1281],{"className":1280,"style":1078},[901],[571,1282],{}," mit den Einträgen ",[571,1285,1287,1325],{"className":1286},[574],[571,1288,1290],{"className":1289},[578],[580,1291,1292],{"xmlns":582},[584,1293,1294,1322],{},[587,1295,1296],{},[1297,1298,1299,1311],"mfrac",{},[587,1300,1301,1304],{},[590,1302,1303],{"mathvariant":800},"∂",[830,1305,1306,1308],{},[590,1307,592],{},[590,1309,1310],{},"i",[587,1312,1313,1315],{},[590,1314,1303],{"mathvariant":800},[830,1316,1317,1319],{},[590,1318,600],{},[590,1320,1321],{},"j",[612,1323,1324],{"encoding":614},"\\frac{\\partial F_i}{\\partial x_j}",[571,1326,1328],{"className":1327,"ariaHidden":620},[619],[571,1329,1331,1335],{"className":1330},[624],[571,1332],{"className":1333,"style":1334},[628],"height:1.4385em;vertical-align:-0.5423em;",[571,1336,1338,1342,1499],{"className":1337},[633],[571,1339],{"className":1340},[639,1341],"nulldelimiter",[571,1343,1345],{"className":1344},[1297],[571,1346,1348,1490],{"className":1347},[893,1047],[571,1349,1351,1487],{"className":1350},[897],[571,1352,1355,1419,1430],{"className":1353,"style":1354},[901],"height:0.8962em;",[571,1356,1358,1362],{"style":1357},"top:-2.655em;",[571,1359],{"className":1360,"style":1361},[909],"height:3em;",[571,1363,1365],{"className":1364},[914,915,916,917],[571,1366,1368,1372],{"className":1367},[633,917],[571,1369,1303],{"className":1370,"style":1371},[633,917],"margin-right:0.0556em;",[571,1373,1375,1378],{"className":1374},[633,917],[571,1376,600],{"className":1377},[633,634,917],[571,1379,1381],{"className":1380},[889],[571,1382,1384,1410],{"className":1383},[893,1047],[571,1385,1387,1407],{"className":1386},[897],[571,1388,1391],{"className":1389,"style":1390},[901],"height:0.3281em;",[571,1392,1394,1398],{"style":1393},"top:-2.357em;margin-left:0em;margin-right:0.0714em;",[571,1395],{"className":1396,"style":1397},[909],"height:2.5em;",[571,1399,1403],{"className":1400},[914,1401,1402,917],"reset-size3","size1",[571,1404,1321],{"className":1405,"style":1406},[633,634,917],"margin-right:0.0572em;",[571,1408,1071],{"className":1409},[1070],[571,1411,1413],{"className":1412},[897],[571,1414,1417],{"className":1415,"style":1416},[901],"height:0.2819em;",[571,1418],{},[571,1420,1422,1425],{"style":1421},"top:-3.23em;",[571,1423],{"className":1424,"style":1361},[909],[571,1426],{"className":1427,"style":1429},[1428],"frac-line","border-bottom-width:0.04em;",[571,1431,1433,1436],{"style":1432},"top:-3.4101em;",[571,1434],{"className":1435,"style":1361},[909],[571,1437,1439],{"className":1438},[914,915,916,917],[571,1440,1442,1445],{"className":1441},[633,917],[571,1443,1303],{"className":1444,"style":1371},[633,917],[571,1446,1448,1451],{"className":1447},[633,917],[571,1449,592],{"className":1450,"style":635},[633,634,917],[571,1452,1454],{"className":1453},[889],[571,1455,1457,1478],{"className":1456},[893,1047],[571,1458,1460,1475],{"className":1459},[897],[571,1461,1463],{"className":1462,"style":1390},[901],[571,1464,1466,1469],{"style":1465},"top:-2.357em;margin-left:-0.1389em;margin-right:0.0714em;",[571,1467],{"className":1468,"style":1397},[909],[571,1470,1472],{"className":1471},[914,1401,1402,917],[571,1473,1310],{"className":1474},[633,634,917],[571,1476,1071],{"className":1477},[1070],[571,1479,1481],{"className":1480},[897],[571,1482,1485],{"className":1483,"style":1484},[901],"height:0.143em;",[571,1486],{},[571,1488,1071],{"className":1489},[1070],[571,1491,1493],{"className":1492},[897],[571,1494,1497],{"className":1495,"style":1496},[901],"height:0.5423em;",[571,1498],{},[571,1500],{"className":1501},[646,1341],".",[563,1504,1505,1506,1891,1892,1971],{},"Formal ist ",[571,1507,1509,1603],{"className":1508},[574],[571,1510,1512],{"className":1511},[578],[580,1513,1514],{"xmlns":582},[584,1515,1516,1600],{},[587,1517,1518,1535,1537,1549,1552,1558,1560,1572,1582,1584,1586,1598],{},[782,1519,1520,1522],{},[590,1521,600],{},[587,1523,1524,1526,1528,1530,1533],{},[594,1525,597],{"stretchy":596},[590,1527,792],{},[594,1529,797],{},[608,1531,1532],{},"1",[594,1534,603],{"stretchy":596},[594,1536,606],{},[782,1538,1539,1541],{},[590,1540,600],{},[587,1542,1543,1545,1547],{},[594,1544,597],{"stretchy":596},[590,1546,792],{},[594,1548,603],{"stretchy":596},[594,1550,1551],{},"−",[830,1553,1554,1556],{},[590,1555,834],{},[590,1557,592],{},[594,1559,597],{"stretchy":596},[782,1561,1562,1564],{},[590,1563,600],{},[587,1565,1566,1568,1570],{},[594,1567,597],{"stretchy":596},[590,1569,792],{},[594,1571,603],{"stretchy":596},[782,1573,1574,1576],{},[594,1575,603],{"stretchy":596},[587,1577,1578,1580],{},[594,1579,1551],{},[608,1581,1532],{},[590,1583,592],{},[594,1585,597],{"stretchy":596},[782,1587,1588,1590],{},[590,1589,600],{},[587,1591,1592,1594,1596],{},[594,1593,597],{"stretchy":596},[590,1595,792],{},[594,1597,603],{"stretchy":596},[594,1599,603],{"stretchy":596},[612,1601,1602],{"encoding":614},"x^{(k+1)} = x^{(k)} - J_F(x^{(k)})^{-1} F(x^{(k)})",[571,1604,1606,1666,1720],{"className":1605,"ariaHidden":620},[619],[571,1607,1609,1613,1657,1660,1663],{"className":1608},[624],[571,1610],{"className":1611,"style":1612},[628],"height:0.888em;",[571,1614,1616,1619],{"className":1615},[633],[571,1617,600],{"className":1618},[633,634],[571,1620,1622],{"className":1621},[889],[571,1623,1625],{"className":1624},[893],[571,1626,1628],{"className":1627},[897],[571,1629,1631],{"className":1630,"style":1612},[901],[571,1632,1633,1636],{"style":1194},[571,1634],{"className":1635,"style":910},[909],[571,1637,1639],{"className":1638},[914,915,916,917],[571,1640,1642,1645,1648,1651,1654],{"className":1641},[633,917],[571,1643,597],{"className":1644},[639,917],[571,1646,792],{"className":1647,"style":927},[633,634,917],[571,1649,797],{"className":1650},[938,917],[571,1652,1532],{"className":1653},[633,917],[571,1655,603],{"className":1656},[646,917],[571,1658],{"className":1659,"style":651},[650],[571,1661,606],{"className":1662},[655],[571,1664],{"className":1665,"style":651},[650],[571,1667,1669,1673,1711,1714,1717],{"className":1668},[624],[571,1670],{"className":1671,"style":1672},[628],"height:0.9713em;vertical-align:-0.0833em;",[571,1674,1676,1679],{"className":1675},[633],[571,1677,600],{"className":1678},[633,634],[571,1680,1682],{"className":1681},[889],[571,1683,1685],{"className":1684},[893],[571,1686,1688],{"className":1687},[897],[571,1689,1691],{"className":1690,"style":1612},[901],[571,1692,1693,1696],{"style":1194},[571,1694],{"className":1695,"style":910},[909],[571,1697,1699],{"className":1698},[914,915,916,917],[571,1700,1702,1705,1708],{"className":1701},[633,917],[571,1703,597],{"className":1704},[639,917],[571,1706,792],{"className":1707,"style":927},[633,634,917],[571,1709,603],{"className":1710},[646,917],[571,1712],{"className":1713,"style":934},[650],[571,1715,1551],{"className":1716},[938],[571,1718],{"className":1719,"style":934},[650],[571,1721,1723,1727,1767,1770,1808,1844,1847,1850,1888],{"className":1722},[624],[571,1724],{"className":1725,"style":1726},[628],"height:1.138em;vertical-align:-0.25em;",[571,1728,1730,1733],{"className":1729},[633],[571,1731,834],{"className":1732,"style":1040},[633,634],[571,1734,1736],{"className":1735},[889],[571,1737,1739,1759],{"className":1738},[893,1047],[571,1740,1742,1756],{"className":1741},[897],[571,1743,1745],{"className":1744,"style":1054},[901],[571,1746,1747,1750],{"style":1057},[571,1748],{"className":1749,"style":910},[909],[571,1751,1753],{"className":1752},[914,915,916,917],[571,1754,592],{"className":1755,"style":635},[633,634,917],[571,1757,1071],{"className":1758},[1070],[571,1760,1762],{"className":1761},[897],[571,1763,1765],{"className":1764,"style":1078},[901],[571,1766],{},[571,1768,597],{"className":1769},[639],[571,1771,1773,1776],{"className":1772},[633],[571,1774,600],{"className":1775},[633,634],[571,1777,1779],{"className":1778},[889],[571,1780,1782],{"className":1781},[893],[571,1783,1785],{"className":1784},[897],[571,1786,1788],{"className":1787,"style":1612},[901],[571,1789,1790,1793],{"style":1194},[571,1791],{"className":1792,"style":910},[909],[571,1794,1796],{"className":1795},[914,915,916,917],[571,1797,1799,1802,1805],{"className":1798},[633,917],[571,1800,597],{"className":1801},[639,917],[571,1803,792],{"className":1804,"style":927},[633,634,917],[571,1806,603],{"className":1807},[646,917],[571,1809,1811,1814],{"className":1810},[646],[571,1812,603],{"className":1813},[646],[571,1815,1817],{"className":1816},[889],[571,1818,1820],{"className":1819},[893],[571,1821,1823],{"className":1822},[897],[571,1824,1827],{"className":1825,"style":1826},[901],"height:0.8141em;",[571,1828,1829,1832],{"style":1194},[571,1830],{"className":1831,"style":910},[909],[571,1833,1835],{"className":1834},[914,915,916,917],[571,1836,1838,1841],{"className":1837},[633,917],[571,1839,1551],{"className":1840},[633,917],[571,1842,1532],{"className":1843},[633,917],[571,1845,592],{"className":1846,"style":635},[633,634],[571,1848,597],{"className":1849},[639],[571,1851,1853,1856],{"className":1852},[633],[571,1854,600],{"className":1855},[633,634],[571,1857,1859],{"className":1858},[889],[571,1860,1862],{"className":1861},[893],[571,1863,1865],{"className":1864},[897],[571,1866,1868],{"className":1867,"style":1612},[901],[571,1869,1870,1873],{"style":1194},[571,1871],{"className":1872,"style":910},[909],[571,1874,1876],{"className":1875},[914,915,916,917],[571,1877,1879,1882,1885],{"className":1878},[633,917],[571,1880,597],{"className":1881},[639,917],[571,1883,792],{"className":1884,"style":927},[633,634,917],[571,1886,603],{"className":1887},[646,917],[571,1889,603],{"className":1890},[646],". Man berechnet die Inverse aber nicht, sondern löst in jedem Schritt das lineare Gleichungssystem für ",[571,1893,1895,1921],{"className":1894},[574],[571,1896,1898],{"className":1897},[578],[580,1899,1900],{"xmlns":582},[584,1901,1902,1918],{},[587,1903,1904,1906],{},[590,1905,801],{"mathvariant":800},[782,1907,1908,1910],{},[590,1909,600],{},[587,1911,1912,1914,1916],{},[594,1913,597],{"stretchy":596},[590,1915,792],{},[594,1917,603],{"stretchy":596},[612,1919,1920],{"encoding":614},"\\Delta x^{(k)}",[571,1922,1924],{"className":1923,"ariaHidden":620},[619],[571,1925,1927,1930,1933],{"className":1926},[624],[571,1928],{"className":1929,"style":1612},[628],[571,1931,801],{"className":1932},[633],[571,1934,1936,1939],{"className":1935},[633],[571,1937,600],{"className":1938},[633,634],[571,1940,1942],{"className":1941},[889],[571,1943,1945],{"className":1944},[893],[571,1946,1948],{"className":1947},[897],[571,1949,1951],{"className":1950,"style":1612},[901],[571,1952,1953,1956],{"style":1194},[571,1954],{"className":1955,"style":910},[909],[571,1957,1959],{"className":1958},[914,915,916,917],[571,1960,1962,1965,1968],{"className":1961},[633,917],[571,1963,597],{"className":1964},[639,917],[571,1966,792],{"className":1967,"style":927},[633,634,917],[571,1969,603],{"className":1970},[646,917],", z.B. mit LU-Zerlegung.",[563,1973,1974],{},"Eigenschaften:",[1976,1977,1978,1985,2304],"ul",{},[1979,1980,1981,1984],"li",{},[567,1982,1983],{},"Quadratische Konvergenz",", wenn der Startwert nahe genug an einer Nullstelle liegt und die Jacobi-Matrix dort invertierbar und Lipschitz-stetig ist.",[1979,1986,1987,1988,1991,1992,669,2227,1502],{},"Ohne guten Startwert kann das Verfahren divergieren. Abhilfe schafft eine ",[567,1989,1990],{},"Dämpfung",": ",[571,1993,1995,2058],{"className":1994},[574],[571,1996,1998],{"className":1997},[578],[580,1999,2000],{"xmlns":582},[584,2001,2002,2055],{},[587,2003,2004,2020,2022,2034,2036,2039,2041,2043],{},[782,2005,2006,2008],{},[590,2007,600],{},[587,2009,2010,2012,2014,2016,2018],{},[594,2011,597],{"stretchy":596},[590,2013,792],{},[594,2015,797],{},[608,2017,1532],{},[594,2019,603],{"stretchy":596},[594,2021,606],{},[782,2023,2024,2026],{},[590,2025,600],{},[587,2027,2028,2030,2032],{},[594,2029,597],{"stretchy":596},[590,2031,792],{},[594,2033,603],{"stretchy":596},[594,2035,797],{},[590,2037,2038],{},"τ",[854,2040,856],{},[590,2042,801],{"mathvariant":800},[782,2044,2045,2047],{},[590,2046,600],{},[587,2048,2049,2051,2053],{},[594,2050,597],{"stretchy":596},[590,2052,792],{},[594,2054,603],{"stretchy":596},[612,2056,2057],{"encoding":614},"x^{(k+1)} = x^{(k)} + \\tau\\,\\Delta x^{(k)}",[571,2059,2061,2120,2173],{"className":2060,"ariaHidden":620},[619],[571,2062,2064,2067,2111,2114,2117],{"className":2063},[624],[571,2065],{"className":2066,"style":1612},[628],[571,2068,2070,2073],{"className":2069},[633],[571,2071,600],{"className":2072},[633,634],[571,2074,2076],{"className":2075},[889],[571,2077,2079],{"className":2078},[893],[571,2080,2082],{"className":2081},[897],[571,2083,2085],{"className":2084,"style":1612},[901],[571,2086,2087,2090],{"style":1194},[571,2088],{"className":2089,"style":910},[909],[571,2091,2093],{"className":2092},[914,915,916,917],[571,2094,2096,2099,2102,2105,2108],{"className":2095},[633,917],[571,2097,597],{"className":2098},[639,917],[571,2100,792],{"className":2101,"style":927},[633,634,917],[571,2103,797],{"className":2104},[938,917],[571,2106,1532],{"className":2107},[633,917],[571,2109,603],{"className":2110},[646,917],[571,2112],{"className":2113,"style":651},[650],[571,2115,606],{"className":2116},[655],[571,2118],{"className":2119,"style":651},[650],[571,2121,2123,2126,2164,2167,2170],{"className":2122},[624],[571,2124],{"className":2125,"style":1672},[628],[571,2127,2129,2132],{"className":2128},[633],[571,2130,600],{"className":2131},[633,634],[571,2133,2135],{"className":2134},[889],[571,2136,2138],{"className":2137},[893],[571,2139,2141],{"className":2140},[897],[571,2142,2144],{"className":2143,"style":1612},[901],[571,2145,2146,2149],{"style":1194},[571,2147],{"className":2148,"style":910},[909],[571,2150,2152],{"className":2151},[914,915,916,917],[571,2153,2155,2158,2161],{"className":2154},[633,917],[571,2156,597],{"className":2157},[639,917],[571,2159,792],{"className":2160,"style":927},[633,634,917],[571,2162,603],{"className":2163},[646,917],[571,2165],{"className":2166,"style":934},[650],[571,2168,797],{"className":2169},[938],[571,2171],{"className":2172,"style":934},[650],[571,2174,2176,2179,2183,2186,2189],{"className":2175},[624],[571,2177],{"className":2178,"style":1612},[628],[571,2180,2038],{"className":2181,"style":2182},[633,634],"margin-right:0.1132em;",[571,2184],{"className":2185,"style":1128},[650],[571,2187,801],{"className":2188},[633],[571,2190,2192,2195],{"className":2191},[633],[571,2193,600],{"className":2194},[633,634],[571,2196,2198],{"className":2197},[889],[571,2199,2201],{"className":2200},[893],[571,2202,2204],{"className":2203},[897],[571,2205,2207],{"className":2206,"style":1612},[901],[571,2208,2209,2212],{"style":1194},[571,2210],{"className":2211,"style":910},[909],[571,2213,2215],{"className":2214},[914,915,916,917],[571,2216,2218,2221,2224],{"className":2217},[633,917],[571,2219,597],{"className":2220},[639,917],[571,2222,792],{"className":2223,"style":927},[633,634,917],[571,2225,603],{"className":2226},[646,917],[571,2228,2230,2254],{"className":2229},[574],[571,2231,2233],{"className":2232},[578],[580,2234,2235],{"xmlns":582},[584,2236,2237,2251],{},[587,2238,2239,2241,2244,2246,2249],{},[608,2240,610],{},[594,2242,2243],{},"\u003C",[590,2245,2038],{},[594,2247,2248],{},"≤",[608,2250,1532],{},[612,2252,2253],{"encoding":614},"0 \u003C \\tau \\leq 1",[571,2255,2257,2276,2295],{"className":2256,"ariaHidden":620},[619],[571,2258,2260,2264,2267,2270,2273],{"className":2259},[624],[571,2261],{"className":2262,"style":2263},[628],"height:0.6835em;vertical-align:-0.0391em;",[571,2265,610],{"className":2266},[633],[571,2268],{"className":2269,"style":651},[650],[571,2271,2243],{"className":2272},[655],[571,2274],{"className":2275,"style":651},[650],[571,2277,2279,2283,2286,2289,2292],{"className":2278},[624],[571,2280],{"className":2281,"style":2282},[628],"height:0.7719em;vertical-align:-0.136em;",[571,2284,2038],{"className":2285,"style":2182},[633,634],[571,2287],{"className":2288,"style":651},[650],[571,2290,2248],{"className":2291},[655],[571,2293],{"className":2294,"style":651},[650],[571,2296,2298,2301],{"className":2297},[624],[571,2299],{"className":2300,"style":665},[628],[571,2302,1532],{"className":2303},[633],[1979,2305,2306],{},"Pro Schritt muss man die Jacobi-Matrix aufstellen und ein lineares System lösen. Vereinfachte Varianten verwenden dieselbe Matrix für mehrere Schritte.",[563,2308,2309,2310,2398,2399,2498],{},"Abbruch typischerweise, wenn ",[571,2311,2313,2344],{"className":2312},[574],[571,2314,2316],{"className":2315},[578],[580,2317,2318],{"xmlns":582},[584,2319,2320,2341],{},[587,2321,2322,2325,2327,2339],{},[590,2323,2324],{"mathvariant":800},"∥",[590,2326,801],{"mathvariant":800},[782,2328,2329,2331],{},[590,2330,600],{},[587,2332,2333,2335,2337],{},[594,2334,597],{"stretchy":596},[590,2336,792],{},[594,2338,603],{"stretchy":596},[590,2340,2324],{"mathvariant":800},[612,2342,2343],{"encoding":614},"\\|\\Delta x^{(k)}\\|",[571,2345,2347],{"className":2346,"ariaHidden":620},[619],[571,2348,2350,2353,2357,2395],{"className":2349},[624],[571,2351],{"className":2352,"style":1726},[628],[571,2354,2356],{"className":2355},[633],"∥Δ",[571,2358,2360,2363],{"className":2359},[633],[571,2361,600],{"className":2362},[633,634],[571,2364,2366],{"className":2365},[889],[571,2367,2369],{"className":2368},[893],[571,2370,2372],{"className":2371},[897],[571,2373,2375],{"className":2374,"style":1612},[901],[571,2376,2377,2380],{"style":1194},[571,2378],{"className":2379,"style":910},[909],[571,2381,2383],{"className":2382},[914,915,916,917],[571,2384,2386,2389,2392],{"className":2385},[633,917],[571,2387,597],{"className":2388},[639,917],[571,2390,792],{"className":2391,"style":927},[633,634,917],[571,2393,603],{"className":2394},[646,917],[571,2396,2324],{"className":2397},[633]," oder ",[571,2400,2402,2436],{"className":2401},[574],[571,2403,2405],{"className":2404},[578],[580,2406,2407],{"xmlns":582},[584,2408,2409,2433],{},[587,2410,2411,2413,2415,2417,2429,2431],{},[590,2412,2324],{"mathvariant":800},[590,2414,592],{},[594,2416,597],{"stretchy":596},[782,2418,2419,2421],{},[590,2420,600],{},[587,2422,2423,2425,2427],{},[594,2424,597],{"stretchy":596},[590,2426,792],{},[594,2428,603],{"stretchy":596},[594,2430,603],{"stretchy":596},[590,2432,2324],{"mathvariant":800},[612,2434,2435],{"encoding":614},"\\|F(x^{(k)})\\|",[571,2437,2439],{"className":2438,"ariaHidden":620},[619],[571,2440,2442,2445,2448,2451,2454,2492,2495],{"className":2441},[624],[571,2443],{"className":2444,"style":1726},[628],[571,2446,2324],{"className":2447},[633],[571,2449,592],{"className":2450,"style":635},[633,634],[571,2452,597],{"className":2453},[639],[571,2455,2457,2460],{"className":2456},[633],[571,2458,600],{"className":2459},[633,634],[571,2461,2463],{"className":2462},[889],[571,2464,2466],{"className":2465},[893],[571,2467,2469],{"className":2468},[897],[571,2470,2472],{"className":2471,"style":1612},[901],[571,2473,2474,2477],{"style":1194},[571,2475],{"className":2476,"style":910},[909],[571,2478,2480],{"className":2479},[914,915,916,917],[571,2481,2483,2486,2489],{"className":2482},[633,917],[571,2484,597],{"className":2485},[639,917],[571,2487,792],{"className":2488,"style":927},[633,634,917],[571,2490,603],{"className":2491},[646,917],[571,2493,603],{"className":2494},[646],[571,2496,2324],{"className":2497},[633]," klein genug ist.",[558,2500,2502],{"id":2501},"beispiele","Beispiele",[563,2504,2505],{},"Gesucht ist eine Lösung von",[571,2507,2509],{"className":2508},[763],[571,2510,2512,2674],{"className":2511},[574],[571,2513,2515],{"className":2514},[578],[580,2516,2517],{"xmlns":582,"display":772},[584,2518,2519,2671],{},[587,2520,2521,2523,2525,2527,2530,2533,2535,2537,2599,2601,2603,2605,2608,2614,2616,2618,2620,2622,2624,2626],{},[590,2522,592],{},[594,2524,597],{"stretchy":596},[590,2526,600],{},[594,2528,2529],{"separator":620},",",[590,2531,2532],{},"y",[594,2534,603],{"stretchy":596},[594,2536,606],{},[587,2538,2539,2541,2597],{},[594,2540,597],{"fence":620},[2542,2543,2547,2574],"mtable",{"rowspacing":2544,"columnalign":2545,"columnspacing":2546},"0.16em","center","1em",[2548,2549,2550],"mtr",{},[2551,2552,2553],"mtd",{},[2554,2555,2556],"mstyle",{"scriptlevel":610,"displaystyle":596},[587,2557,2558,2565,2567,2569,2571],{},[782,2559,2560,2562],{},[590,2561,600],{},[608,2563,2564],{},"2",[594,2566,797],{},[590,2568,2532],{},[594,2570,1551],{},[608,2572,2573],{},"3",[2548,2575,2576],{},[2551,2577,2578],{},[2554,2579,2580],{"scriptlevel":610,"displaystyle":596},[587,2581,2582,2584,2586,2592,2594],{},[590,2583,600],{},[594,2585,797],{},[782,2587,2588,2590],{},[590,2589,2532],{},[608,2591,2564],{},[594,2593,1551],{},[608,2595,2596],{},"5",[594,2598,603],{"fence":620},[594,2600,606],{},[608,2602,610],{},[594,2604,2529],{"separator":620},[650,2606],{"width":2607},"2em",[830,2609,2610,2612],{},[590,2611,834],{},[590,2613,592],{},[594,2615,597],{"stretchy":596},[590,2617,600],{},[594,2619,2529],{"separator":620},[590,2621,2532],{},[594,2623,603],{"stretchy":596},[594,2625,606],{},[587,2627,2628,2630,2669],{},[594,2629,597],{"fence":620},[2542,2631,2633,2651],{"rowspacing":2544,"columnalign":2632,"columnspacing":2546},"center center",[2548,2634,2635,2645],{},[2551,2636,2637],{},[2554,2638,2639],{"scriptlevel":610,"displaystyle":596},[587,2640,2641,2643],{},[608,2642,2564],{},[590,2644,600],{},[2551,2646,2647],{},[2554,2648,2649],{"scriptlevel":610,"displaystyle":596},[608,2650,1532],{},[2548,2652,2653,2659],{},[2551,2654,2655],{},[2554,2656,2657],{"scriptlevel":610,"displaystyle":596},[608,2658,1532],{},[2551,2660,2661],{},[2554,2662,2663],{"scriptlevel":610,"displaystyle":596},[587,2664,2665,2667],{},[608,2666,2564],{},[590,2668,2532],{},[594,2670,603],{"fence":620},[612,2672,2673],{"encoding":614},"F(x, y) = \\begin{pmatrix} x^2 + y - 3 \\\\ x + y^2 - 5 \\end{pmatrix} = 0, \\qquad J_F(x, y) = \\begin{pmatrix} 2x & 1 \\\\ 1 & 2y \\end{pmatrix}",[571,2675,2677,2715,2906,2992],{"className":2676,"ariaHidden":620},[619],[571,2678,2680,2683,2686,2689,2692,2696,2699,2703,2706,2709,2712],{"className":2679},[624],[571,2681],{"className":2682,"style":629},[628],[571,2684,592],{"className":2685,"style":635},[633,634],[571,2687,597],{"className":2688},[639],[571,2690,600],{"className":2691},[633,634],[571,2693,2529],{"className":2694},[2695],"mpunct",[571,2697],{"className":2698,"style":1128},[650],[571,2700,2532],{"className":2701,"style":2702},[633,634],"margin-right:0.0359em;",[571,2704,603],{"className":2705},[646],[571,2707],{"className":2708,"style":651},[650],[571,2710,606],{"className":2711},[655],[571,2713],{"className":2714,"style":651},[650],[571,2716,2718,2722,2897,2900,2903],{"className":2717},[624],[571,2719],{"className":2720,"style":2721},[628],"height:2.4em;vertical-align:-0.95em;",[571,2723,2726,2735,2891],{"className":2724},[2725],"minner",[571,2727,2731],{"className":2728,"style":2730},[639,2729],"delimcenter","top:0em;",[571,2732,597],{"className":2733},[2734,916],"delimsizing",[571,2736,2738],{"className":2737},[633],[571,2739,2741],{"className":2740},[2542],[571,2742,2745],{"className":2743},[2744],"col-align-c",[571,2746,2748,2882],{"className":2747},[893,1047],[571,2749,2751,2879],{"className":2750},[897],[571,2752,2755,2817],{"className":2753,"style":2754},[901],"height:1.45em;",[571,2756,2758,2761],{"style":2757},"top:-3.61em;",[571,2759],{"className":2760,"style":1361},[909],[571,2762,2764,2793,2796,2799,2802,2805,2808,2811,2814],{"className":2763},[633],[571,2765,2767,2770],{"className":2766},[633],[571,2768,600],{"className":2769},[633,634],[571,2771,2773],{"className":2772},[889],[571,2774,2776],{"className":2775},[893],[571,2777,2779],{"className":2778},[897],[571,2780,2782],{"className":2781,"style":1826},[901],[571,2783,2784,2787],{"style":1194},[571,2785],{"className":2786,"style":910},[909],[571,2788,2790],{"className":2789},[914,915,916,917],[571,2791,2564],{"className":2792},[633,917],[571,2794],{"className":2795,"style":934},[650],[571,2797,797],{"className":2798},[938],[571,2800],{"className":2801,"style":934},[650],[571,2803,2532],{"className":2804,"style":2702},[633,634],[571,2806],{"className":2807,"style":934},[650],[571,2809,1551],{"className":2810},[938],[571,2812],{"className":2813,"style":934},[650],[571,2815,2573],{"className":2816},[633],[571,2818,2820,2823],{"style":2819},"top:-2.41em;",[571,2821],{"className":2822,"style":1361},[909],[571,2824,2826,2829,2832,2835,2838,2867,2870,2873,2876],{"className":2825},[633],[571,2827,600],{"className":2828},[633,634],[571,2830],{"className":2831,"style":934},[650],[571,2833,797],{"className":2834},[938],[571,2836],{"className":2837,"style":934},[650],[571,2839,2841,2844],{"className":2840},[633],[571,2842,2532],{"className":2843,"style":2702},[633,634],[571,2845,2847],{"className":2846},[889],[571,2848,2850],{"className":2849},[893],[571,2851,2853],{"className":2852},[897],[571,2854,2856],{"className":2855,"style":1826},[901],[571,2857,2858,2861],{"style":1194},[571,2859],{"className":2860,"style":910},[909],[571,2862,2864],{"className":2863},[914,915,916,917],[571,2865,2564],{"className":2866},[633,917],[571,2868],{"className":2869,"style":934},[650],[571,2871,1551],{"className":2872},[938],[571,2874],{"className":2875,"style":934},[650],[571,2877,2596],{"className":2878},[633],[571,2880,1071],{"className":2881},[1070],[571,2883,2885],{"className":2884},[897],[571,2886,2889],{"className":2887,"style":2888},[901],"height:0.95em;",[571,2890],{},[571,2892,2894],{"className":2893,"style":2730},[646,2729],[571,2895,603],{"className":2896},[2734,916],[571,2898],{"className":2899,"style":651},[650],[571,2901,606],{"className":2902},[655],[571,2904],{"className":2905,"style":651},[650],[571,2907,2909,2912,2915,2918,2922,2925,2965,2968,2971,2974,2977,2980,2983,2986,2989],{"className":2908},[624],[571,2910],{"className":2911,"style":629},[628],[571,2913,610],{"className":2914},[633],[571,2916,2529],{"className":2917},[2695],[571,2919],{"className":2920,"style":2921},[650],"margin-right:2em;",[571,2923],{"className":2924,"style":1128},[650],[571,2926,2928,2931],{"className":2927},[633],[571,2929,834],{"className":2930,"style":1040},[633,634],[571,2932,2934],{"className":2933},[889],[571,2935,2937,2957],{"className":2936},[893,1047],[571,2938,2940,2954],{"className":2939},[897],[571,2941,2943],{"className":2942,"style":1054},[901],[571,2944,2945,2948],{"style":1057},[571,2946],{"className":2947,"style":910},[909],[571,2949,2951],{"className":2950},[914,915,916,917],[571,2952,592],{"className":2953,"style":635},[633,634,917],[571,2955,1071],{"className":2956},[1070],[571,2958,2960],{"className":2959},[897],[571,2961,2963],{"className":2962,"style":1078},[901],[571,2964],{},[571,2966,597],{"className":2967},[639],[571,2969,600],{"className":2970},[633,634],[571,2972,2529],{"className":2973},[2695],[571,2975],{"className":2976,"style":1128},[650],[571,2978,2532],{"className":2979,"style":2702},[633,634],[571,2981,603],{"className":2982},[646],[571,2984],{"className":2985,"style":651},[650],[571,2987,606],{"className":2988},[655],[571,2990],{"className":2991,"style":651},[650],[571,2993,2995,2998],{"className":2994},[624],[571,2996],{"className":2997,"style":2721},[628],[571,2999,3001,3007,3117],{"className":3000},[2725],[571,3002,3004],{"className":3003,"style":2730},[639,2729],[571,3005,597],{"className":3006},[2734,916],[571,3008,3010],{"className":3009},[633],[571,3011,3013,3061,3066,3069],{"className":3012},[2542],[571,3014,3016],{"className":3015},[2744],[571,3017,3019,3053],{"className":3018},[893,1047],[571,3020,3022,3050],{"className":3021},[897],[571,3023,3025,3039],{"className":3024,"style":2754},[901],[571,3026,3027,3030],{"style":2757},[571,3028],{"className":3029,"style":1361},[909],[571,3031,3033,3036],{"className":3032},[633],[571,3034,2564],{"className":3035},[633],[571,3037,600],{"className":3038},[633,634],[571,3040,3041,3044],{"style":2819},[571,3042],{"className":3043,"style":1361},[909],[571,3045,3047],{"className":3046},[633],[571,3048,1532],{"className":3049},[633],[571,3051,1071],{"className":3052},[1070],[571,3054,3056],{"className":3055},[897],[571,3057,3059],{"className":3058,"style":2888},[901],[571,3060],{},[571,3062],{"className":3063,"style":3065},[3064],"arraycolsep","width:0.5em;",[571,3067],{"className":3068,"style":3065},[3064],[571,3070,3072],{"className":3071},[2744],[571,3073,3075,3109],{"className":3074},[893,1047],[571,3076,3078,3106],{"className":3077},[897],[571,3079,3081,3092],{"className":3080,"style":2754},[901],[571,3082,3083,3086],{"style":2757},[571,3084],{"className":3085,"style":1361},[909],[571,3087,3089],{"className":3088},[633],[571,3090,1532],{"className":3091},[633],[571,3093,3094,3097],{"style":2819},[571,3095],{"className":3096,"style":1361},[909],[571,3098,3100,3103],{"className":3099},[633],[571,3101,2564],{"className":3102},[633],[571,3104,2532],{"className":3105,"style":2702},[633,634],[571,3107,1071],{"className":3108},[1070],[571,3110,3112],{"className":3111},[897],[571,3113,3115],{"className":3114,"style":2888},[901],[571,3116],{},[571,3118,3120],{"className":3119,"style":2730},[646,2729],[571,3121,603],{"className":3122},[2734,916],[563,3124,3125,3126,3178,3179,1991,3231,3322],{},"Eine Lösung ist ",[571,3127,3129,3151],{"className":3128},[574],[571,3130,3132],{"className":3131},[578],[580,3133,3134],{"xmlns":582},[584,3135,3136,3148],{},[587,3137,3138,3140,3142,3144,3146],{},[594,3139,597],{"stretchy":596},[608,3141,1532],{},[594,3143,2529],{"separator":620},[608,3145,2564],{},[594,3147,603],{"stretchy":596},[612,3149,3150],{"encoding":614},"(1, 2)",[571,3152,3154],{"className":3153,"ariaHidden":620},[619],[571,3155,3157,3160,3163,3166,3169,3172,3175],{"className":3156},[624],[571,3158],{"className":3159,"style":629},[628],[571,3161,597],{"className":3162},[639],[571,3164,1532],{"className":3165},[633],[571,3167,2529],{"className":3168},[2695],[571,3170],{"className":3171,"style":1128},[650],[571,3173,2564],{"className":3174},[633],[571,3176,603],{"className":3177},[646],". Start bei ",[571,3180,3182,3204],{"className":3181},[574],[571,3183,3185],{"className":3184},[578],[580,3186,3187],{"xmlns":582},[584,3188,3189,3201],{},[587,3190,3191,3193,3195,3197,3199],{},[594,3192,597],{"stretchy":596},[608,3194,1532],{},[594,3196,2529],{"separator":620},[608,3198,1532],{},[594,3200,603],{"stretchy":596},[612,3202,3203],{"encoding":614},"(1, 1)",[571,3205,3207],{"className":3206,"ariaHidden":620},[619],[571,3208,3210,3213,3216,3219,3222,3225,3228],{"className":3209},[624],[571,3211],{"className":3212,"style":629},[628],[571,3214,597],{"className":3215},[639],[571,3217,1532],{"className":3218},[633],[571,3220,2529],{"className":3221},[2695],[571,3223],{"className":3224,"style":1128},[650],[571,3226,1532],{"className":3227},[633],[571,3229,603],{"className":3230},[646],[571,3232,3234,3268],{"className":3233},[574],[571,3235,3237],{"className":3236},[578],[580,3238,3239],{"xmlns":582},[584,3240,3241,3265],{},[587,3242,3243,3245,3247,3249,3251,3253,3256,3259,3261,3263],{},[590,3244,592],{},[594,3246,606],{},[594,3248,597],{"stretchy":596},[594,3250,1551],{},[608,3252,1532],{},[594,3254,3255],{"separator":620},";",[854,3257,3258],{}," ",[594,3260,1551],{},[608,3262,2573],{},[594,3264,603],{"stretchy":596},[612,3266,3267],{"encoding":614},"F = (-1;\\ -3)",[571,3269,3271,3289],{"className":3270,"ariaHidden":620},[619],[571,3272,3274,3277,3280,3283,3286],{"className":3273},[624],[571,3275],{"className":3276,"style":755},[628],[571,3278,592],{"className":3279,"style":635},[633,634],[571,3281],{"className":3282,"style":651},[650],[571,3284,606],{"className":3285},[655],[571,3287],{"className":3288,"style":651},[650],[571,3290,3292,3295,3298,3301,3304,3307,3310,3313,3316,3319],{"className":3291},[624],[571,3293],{"className":3294,"style":629},[628],[571,3296,597],{"className":3297},[639],[571,3299,1551],{"className":3300},[633],[571,3302,1532],{"className":3303},[633],[571,3305,3255],{"className":3306},[2695],[571,3308,3258],{"className":3309},[650],[571,3311],{"className":3312,"style":1128},[650],[571,3314,1551],{"className":3315},[633],[571,3317,2573],{"className":3318},[633],[571,3320,603],{"className":3321},[646],", und das System",[571,3324,3326],{"className":3325},[763],[571,3327,3329,3405],{"className":3328},[574],[571,3330,3332],{"className":3331},[578],[580,3333,3334],{"xmlns":582,"display":772},[584,3335,3336,3402],{},[587,3337,3338,3374,3376,3378],{},[587,3339,3340,3342,3372],{},[594,3341,597],{"fence":620},[2542,3343,3344,3358],{"rowspacing":2544,"columnalign":2632,"columnspacing":2546},[2548,3345,3346,3352],{},[2551,3347,3348],{},[2554,3349,3350],{"scriptlevel":610,"displaystyle":596},[608,3351,2564],{},[2551,3353,3354],{},[2554,3355,3356],{"scriptlevel":610,"displaystyle":596},[608,3357,1532],{},[2548,3359,3360,3366],{},[2551,3361,3362],{},[2554,3363,3364],{"scriptlevel":610,"displaystyle":596},[608,3365,1532],{},[2551,3367,3368],{},[2554,3369,3370],{"scriptlevel":610,"displaystyle":596},[608,3371,2564],{},[594,3373,603],{"fence":620},[590,3375,801],{"mathvariant":800},[594,3377,606],{},[587,3379,3380,3382,3400],{},[594,3381,597],{"fence":620},[2542,3383,3384,3392],{"rowspacing":2544,"columnalign":2545,"columnspacing":2546},[2548,3385,3386],{},[2551,3387,3388],{},[2554,3389,3390],{"scriptlevel":610,"displaystyle":596},[608,3391,1532],{},[2548,3393,3394],{},[2551,3395,3396],{},[2554,3397,3398],{"scriptlevel":610,"displaystyle":596},[608,3399,2573],{},[594,3401,603],{"fence":620},[612,3403,3404],{"encoding":614},"\\begin{pmatrix} 2 & 1 \\\\ 1 & 2 \\end{pmatrix} \\Delta = \\begin{pmatrix} 1 \\\\ 3 \\end{pmatrix}",[571,3406,3408,3546],{"className":3407,"ariaHidden":620},[619],[571,3409,3411,3414,3531,3534,3537,3540,3543],{"className":3410},[624],[571,3412],{"className":3413,"style":2721},[628],[571,3415,3417,3423,3525],{"className":3416},[2725],[571,3418,3420],{"className":3419,"style":2730},[639,2729],[571,3421,597],{"className":3422},[2734,916],[571,3424,3426],{"className":3425},[633],[571,3427,3429,3474,3477,3480],{"className":3428},[2542],[571,3430,3432],{"className":3431},[2744],[571,3433,3435,3466],{"className":3434},[893,1047],[571,3436,3438,3463],{"className":3437},[897],[571,3439,3441,3452],{"className":3440,"style":2754},[901],[571,3442,3443,3446],{"style":2757},[571,3444],{"className":3445,"style":1361},[909],[571,3447,3449],{"className":3448},[633],[571,3450,2564],{"className":3451},[633],[571,3453,3454,3457],{"style":2819},[571,3455],{"className":3456,"style":1361},[909],[571,3458,3460],{"className":3459},[633],[571,3461,1532],{"className":3462},[633],[571,3464,1071],{"className":3465},[1070],[571,3467,3469],{"className":3468},[897],[571,3470,3472],{"className":3471,"style":2888},[901],[571,3473],{},[571,3475],{"className":3476,"style":3065},[3064],[571,3478],{"className":3479,"style":3065},[3064],[571,3481,3483],{"className":3482},[2744],[571,3484,3486,3517],{"className":3485},[893,1047],[571,3487,3489,3514],{"className":3488},[897],[571,3490,3492,3503],{"className":3491,"style":2754},[901],[571,3493,3494,3497],{"style":2757},[571,3495],{"className":3496,"style":1361},[909],[571,3498,3500],{"className":3499},[633],[571,3501,1532],{"className":3502},[633],[571,3504,3505,3508],{"style":2819},[571,3506],{"className":3507,"style":1361},[909],[571,3509,3511],{"className":3510},[633],[571,3512,2564],{"className":3513},[633],[571,3515,1071],{"className":3516},[1070],[571,3518,3520],{"className":3519},[897],[571,3521,3523],{"className":3522,"style":2888},[901],[571,3524],{},[571,3526,3528],{"className":3527,"style":2730},[646,2729],[571,3529,603],{"className":3530},[2734,916],[571,3532],{"className":3533,"style":1128},[650],[571,3535,801],{"className":3536},[633],[571,3538],{"className":3539,"style":651},[650],[571,3541,606],{"className":3542},[655],[571,3544],{"className":3545,"style":651},[650],[571,3547,3549,3552],{"className":3548},[624],[571,3550],{"className":3551,"style":2721},[628],[571,3553,3555,3561,3612],{"className":3554},[2725],[571,3556,3558],{"className":3557,"style":2730},[639,2729],[571,3559,597],{"className":3560},[2734,916],[571,3562,3564],{"className":3563},[633],[571,3565,3567],{"className":3566},[2542],[571,3568,3570],{"className":3569},[2744],[571,3571,3573,3604],{"className":3572},[893,1047],[571,3574,3576,3601],{"className":3575},[897],[571,3577,3579,3590],{"className":3578,"style":2754},[901],[571,3580,3581,3584],{"style":2757},[571,3582],{"className":3583,"style":1361},[909],[571,3585,3587],{"className":3586},[633],[571,3588,1532],{"className":3589},[633],[571,3591,3592,3595],{"style":2819},[571,3593],{"className":3594,"style":1361},[909],[571,3596,3598],{"className":3597},[633],[571,3599,2573],{"className":3600},[633],[571,3602,1071],{"className":3603},[1070],[571,3605,3607],{"className":3606},[897],[571,3608,3610],{"className":3609,"style":2888},[901],[571,3611],{},[571,3613,3615],{"className":3614,"style":2730},[646,2729],[571,3616,603],{"className":3617},[2734,916],[563,3619,3620,3621,3858,3859,1502],{},"hat die Lösung ",[571,3622,3624,3664],{"className":3623},[574],[571,3625,3627],{"className":3626},[578],[580,3628,3629],{"xmlns":582},[584,3630,3631,3661],{},[587,3632,3633,3635,3637],{},[590,3634,801],{"mathvariant":800},[594,3636,606],{},[587,3638,3639,3641,3643,3649,3651,3653,3659],{},[594,3640,597],{"fence":620},[594,3642,1551],{},[1297,3644,3645,3647],{},[608,3646,1532],{},[608,3648,2573],{},[594,3650,3255],{"separator":620},[854,3652,3258],{},[1297,3654,3655,3657],{},[608,3656,2596],{},[608,3658,2573],{},[594,3660,603],{"fence":620},[612,3662,3663],{"encoding":614},"\\Delta = \\left(-\\frac{1}{3};\\ \\frac{5}{3}\\right)",[571,3665,3667,3685],{"className":3666,"ariaHidden":620},[619],[571,3668,3670,3673,3676,3679,3682],{"className":3669},[624],[571,3671],{"className":3672,"style":755},[628],[571,3674,801],{"className":3675},[633],[571,3677],{"className":3678,"style":651},[650],[571,3680,606],{"className":3681},[655],[571,3683],{"className":3684,"style":651},[650],[571,3686,3688,3692],{"className":3687},[624],[571,3689],{"className":3690,"style":3691},[628],"height:1.2em;vertical-align:-0.35em;",[571,3693,3695,3701,3704,3775,3778,3781,3784,3852],{"className":3694},[2725],[571,3696,3698],{"className":3697,"style":2730},[639,2729],[571,3699,597],{"className":3700},[2734,1402],[571,3702,1551],{"className":3703},[633],[571,3705,3707,3710,3772],{"className":3706},[633],[571,3708],{"className":3709},[639,1341],[571,3711,3713],{"className":3712},[1297],[571,3714,3716,3763],{"className":3715},[893,1047],[571,3717,3719,3760],{"className":3718},[897],[571,3720,3723,3737,3745],{"className":3721,"style":3722},[901],"height:0.8451em;",[571,3724,3725,3728],{"style":1357},[571,3726],{"className":3727,"style":1361},[909],[571,3729,3731],{"className":3730},[914,915,916,917],[571,3732,3734],{"className":3733},[633,917],[571,3735,2573],{"className":3736},[633,917],[571,3738,3739,3742],{"style":1421},[571,3740],{"className":3741,"style":1361},[909],[571,3743],{"className":3744,"style":1429},[1428],[571,3746,3748,3751],{"style":3747},"top:-3.394em;",[571,3749],{"className":3750,"style":1361},[909],[571,3752,3754],{"className":3753},[914,915,916,917],[571,3755,3757],{"className":3756},[633,917],[571,3758,1532],{"className":3759},[633,917],[571,3761,1071],{"className":3762},[1070],[571,3764,3766],{"className":3765},[897],[571,3767,3770],{"className":3768,"style":3769},[901],"height:0.345em;",[571,3771],{},[571,3773],{"className":3774},[646,1341],[571,3776,3255],{"className":3777},[2695],[571,3779,3258],{"className":3780},[650],[571,3782],{"className":3783,"style":1128},[650],[571,3785,3787,3790,3849],{"className":3786},[633],[571,3788],{"className":3789},[639,1341],[571,3791,3793],{"className":3792},[1297],[571,3794,3796,3841],{"className":3795},[893,1047],[571,3797,3799,3838],{"className":3798},[897],[571,3800,3802,3816,3824],{"className":3801,"style":3722},[901],[571,3803,3804,3807],{"style":1357},[571,3805],{"className":3806,"style":1361},[909],[571,3808,3810],{"className":3809},[914,915,916,917],[571,3811,3813],{"className":3812},[633,917],[571,3814,2573],{"className":3815},[633,917],[571,3817,3818,3821],{"style":1421},[571,3819],{"className":3820,"style":1361},[909],[571,3822],{"className":3823,"style":1429},[1428],[571,3825,3826,3829],{"style":3747},[571,3827],{"className":3828,"style":1361},[909],[571,3830,3832],{"className":3831},[914,915,916,917],[571,3833,3835],{"className":3834},[633,917],[571,3836,2596],{"className":3837},[633,917],[571,3839,1071],{"className":3840},[1070],[571,3842,3844],{"className":3843},[897],[571,3845,3847],{"className":3846,"style":3769},[901],[571,3848],{},[571,3850],{"className":3851},[646,1341],[571,3853,3855],{"className":3854,"style":2730},[646,2729],[571,3856,603],{"className":3857},[2734,1402],". Neue Näherung: ",[571,3860,3862,3913],{"className":3861},[574],[571,3863,3865],{"className":3864},[578],[580,3866,3867],{"xmlns":582},[584,3868,3869,3910],{},[587,3870,3871,3894,3896,3898,3901,3903,3905,3908],{},[587,3872,3873,3875,3881,3883,3885,3892],{},[594,3874,597],{"fence":620},[1297,3876,3877,3879],{},[608,3878,2564],{},[608,3880,2573],{},[594,3882,3255],{"separator":620},[854,3884,3258],{},[1297,3886,3887,3890],{},[608,3888,3889],{},"8",[608,3891,2573],{},[594,3893,603],{"fence":620},[594,3895,808],{},[594,3897,597],{"stretchy":596},[608,3899,3900],{},"0,6667",[594,3902,3255],{"separator":620},[854,3904,3258],{},[608,3906,3907],{},"2,6667",[594,3909,603],{"stretchy":596},[612,3911,3912],{"encoding":614},"\\left(\\frac{2}{3};\\ \\frac{8}{3}\\right) \\approx (0{,}6667;\\ 2{,}6667)",[571,3914,3916,4091],{"className":3915,"ariaHidden":620},[619],[571,3917,3919,3922,4082,4085,4088],{"className":3918},[624],[571,3920],{"className":3921,"style":3691},[628],[571,3923,3925,3931,3999,4002,4005,4008,4076],{"className":3924},[2725],[571,3926,3928],{"className":3927,"style":2730},[639,2729],[571,3929,597],{"className":3930},[2734,1402],[571,3932,3934,3937,3996],{"className":3933},[633],[571,3935],{"className":3936},[639,1341],[571,3938,3940],{"className":3939},[1297],[571,3941,3943,3988],{"className":3942},[893,1047],[571,3944,3946,3985],{"className":3945},[897],[571,3947,3949,3963,3971],{"className":3948,"style":3722},[901],[571,3950,3951,3954],{"style":1357},[571,3952],{"className":3953,"style":1361},[909],[571,3955,3957],{"className":3956},[914,915,916,917],[571,3958,3960],{"className":3959},[633,917],[571,3961,2573],{"className":3962},[633,917],[571,3964,3965,3968],{"style":1421},[571,3966],{"className":3967,"style":1361},[909],[571,3969],{"className":3970,"style":1429},[1428],[571,3972,3973,3976],{"style":3747},[571,3974],{"className":3975,"style":1361},[909],[571,3977,3979],{"className":3978},[914,915,916,917],[571,3980,3982],{"className":3981},[633,917],[571,3983,2564],{"className":3984},[633,917],[571,3986,1071],{"className":3987},[1070],[571,3989,3991],{"className":3990},[897],[571,3992,3994],{"className":3993,"style":3769},[901],[571,3995],{},[571,3997],{"className":3998},[646,1341],[571,4000,3255],{"className":4001},[2695],[571,4003,3258],{"className":4004},[650],[571,4006],{"className":4007,"style":1128},[650],[571,4009,4011,4014,4073],{"className":4010},[633],[571,4012],{"className":4013},[639,1341],[571,4015,4017],{"className":4016},[1297],[571,4018,4020,4065],{"className":4019},[893,1047],[571,4021,4023,4062],{"className":4022},[897],[571,4024,4026,4040,4048],{"className":4025,"style":3722},[901],[571,4027,4028,4031],{"style":1357},[571,4029],{"className":4030,"style":1361},[909],[571,4032,4034],{"className":4033},[914,915,916,917],[571,4035,4037],{"className":4036},[633,917],[571,4038,2573],{"className":4039},[633,917],[571,4041,4042,4045],{"style":1421},[571,4043],{"className":4044,"style":1361},[909],[571,4046],{"className":4047,"style":1429},[1428],[571,4049,4050,4053],{"style":3747},[571,4051],{"className":4052,"style":1361},[909],[571,4054,4056],{"className":4055},[914,915,916,917],[571,4057,4059],{"className":4058},[633,917],[571,4060,3889],{"className":4061},[633,917],[571,4063,1071],{"className":4064},[1070],[571,4066,4068],{"className":4067},[897],[571,4069,4071],{"className":4070,"style":3769},[901],[571,4072],{},[571,4074],{"className":4075},[646,1341],[571,4077,4079],{"className":4078,"style":2730},[646,2729],[571,4080,603],{"className":4081},[2734,1402],[571,4083],{"className":4084,"style":651},[650],[571,4086,808],{"className":4087},[655],[571,4089],{"className":4090,"style":651},[650],[571,4092,4094,4097,4100,4103,4109,4113,4116,4119,4122,4125,4131,4134],{"className":4093},[624],[571,4095],{"className":4096,"style":629},[628],[571,4098,597],{"className":4099},[639],[571,4101,610],{"className":4102},[633],[571,4104,4106],{"className":4105},[633],[571,4107,2529],{"className":4108},[2695],[571,4110,4112],{"className":4111},[633],"6667",[571,4114,3255],{"className":4115},[2695],[571,4117,3258],{"className":4118},[650],[571,4120],{"className":4121,"style":1128},[650],[571,4123,2564],{"className":4124},[633],[571,4126,4128],{"className":4127},[633],[571,4129,2529],{"className":4130},[2695],[571,4132,4112],{"className":4133},[633],[571,4135,603],{"className":4136},[646],[563,4138,4139,4140,4370,4371,4563,4564,4800],{},"Zweiter Schritt: ",[571,4141,4143,4183],{"className":4142},[574],[571,4144,4146],{"className":4145},[578],[580,4147,4148],{"xmlns":582},[584,4149,4150,4180],{},[587,4151,4152,4154,4156],{},[590,4153,592],{},[594,4155,606],{},[587,4157,4158,4160,4167,4169,4171,4178],{},[594,4159,597],{"fence":620},[1297,4161,4162,4164],{},[608,4163,1532],{},[608,4165,4166],{},"9",[594,4168,3255],{"separator":620},[854,4170,3258],{},[1297,4172,4173,4176],{},[608,4174,4175],{},"25",[608,4177,4166],{},[594,4179,603],{"fence":620},[612,4181,4182],{"encoding":614},"F = \\left(\\frac{1}{9};\\ \\frac{25}{9}\\right)",[571,4184,4186,4204],{"className":4185,"ariaHidden":620},[619],[571,4187,4189,4192,4195,4198,4201],{"className":4188},[624],[571,4190],{"className":4191,"style":755},[628],[571,4193,592],{"className":4194,"style":635},[633,634],[571,4196],{"className":4197,"style":651},[650],[571,4199,606],{"className":4200},[655],[571,4202],{"className":4203,"style":651},[650],[571,4205,4207,4210],{"className":4206},[624],[571,4208],{"className":4209,"style":3691},[628],[571,4211,4213,4219,4287,4290,4293,4296,4364],{"className":4212},[2725],[571,4214,4216],{"className":4215,"style":2730},[639,2729],[571,4217,597],{"className":4218},[2734,1402],[571,4220,4222,4225,4284],{"className":4221},[633],[571,4223],{"className":4224},[639,1341],[571,4226,4228],{"className":4227},[1297],[571,4229,4231,4276],{"className":4230},[893,1047],[571,4232,4234,4273],{"className":4233},[897],[571,4235,4237,4251,4259],{"className":4236,"style":3722},[901],[571,4238,4239,4242],{"style":1357},[571,4240],{"className":4241,"style":1361},[909],[571,4243,4245],{"className":4244},[914,915,916,917],[571,4246,4248],{"className":4247},[633,917],[571,4249,4166],{"className":4250},[633,917],[571,4252,4253,4256],{"style":1421},[571,4254],{"className":4255,"style":1361},[909],[571,4257],{"className":4258,"style":1429},[1428],[571,4260,4261,4264],{"style":3747},[571,4262],{"className":4263,"style":1361},[909],[571,4265,4267],{"className":4266},[914,915,916,917],[571,4268,4270],{"className":4269},[633,917],[571,4271,1532],{"className":4272},[633,917],[571,4274,1071],{"className":4275},[1070],[571,4277,4279],{"className":4278},[897],[571,4280,4282],{"className":4281,"style":3769},[901],[571,4283],{},[571,4285],{"className":4286},[646,1341],[571,4288,3255],{"className":4289},[2695],[571,4291,3258],{"className":4292},[650],[571,4294],{"className":4295,"style":1128},[650],[571,4297,4299,4302,4361],{"className":4298},[633],[571,4300],{"className":4301},[639,1341],[571,4303,4305],{"className":4304},[1297],[571,4306,4308,4353],{"className":4307},[893,1047],[571,4309,4311,4350],{"className":4310},[897],[571,4312,4314,4328,4336],{"className":4313,"style":3722},[901],[571,4315,4316,4319],{"style":1357},[571,4317],{"className":4318,"style":1361},[909],[571,4320,4322],{"className":4321},[914,915,916,917],[571,4323,4325],{"className":4324},[633,917],[571,4326,4166],{"className":4327},[633,917],[571,4329,4330,4333],{"style":1421},[571,4331],{"className":4332,"style":1361},[909],[571,4334],{"className":4335,"style":1429},[1428],[571,4337,4338,4341],{"style":3747},[571,4339],{"className":4340,"style":1361},[909],[571,4342,4344],{"className":4343},[914,915,916,917],[571,4345,4347],{"className":4346},[633,917],[571,4348,4175],{"className":4349},[633,917],[571,4351,1071],{"className":4352},[1070],[571,4354,4356],{"className":4355},[897],[571,4357,4359],{"className":4358,"style":3769},[901],[571,4360],{},[571,4362],{"className":4363},[646,1341],[571,4365,4367],{"className":4366,"style":2730},[646,2729],[571,4368,603],{"className":4369},[2734,1402],", die Jacobi-Matrix ist ",[571,4372,4374,4435],{"className":4373},[574],[571,4375,4377],{"className":4376},[578],[580,4378,4379],{"xmlns":582},[584,4380,4381,4432],{},[587,4382,4383,4385,4430],{},[594,4384,597],{"fence":620},[2542,4386,4387,4409],{"rowspacing":2544,"columnalign":2632,"columnspacing":2546},[2548,4388,4389,4403],{},[2551,4390,4391],{},[2554,4392,4393],{"scriptlevel":610,"displaystyle":596},[587,4394,4395,4398,4401],{},[608,4396,4397],{},"4",[590,4399,4400],{"mathvariant":800},"\u002F",[608,4402,2573],{},[2551,4404,4405],{},[2554,4406,4407],{"scriptlevel":610,"displaystyle":596},[608,4408,1532],{},[2548,4410,4411,4417],{},[2551,4412,4413],{},[2554,4414,4415],{"scriptlevel":610,"displaystyle":596},[608,4416,1532],{},[2551,4418,4419],{},[2554,4420,4421],{"scriptlevel":610,"displaystyle":596},[587,4422,4423,4426,4428],{},[608,4424,4425],{},"16",[590,4427,4400],{"mathvariant":800},[608,4429,2573],{},[594,4431,603],{"fence":620},[612,4433,4434],{"encoding":614},"\\begin{pmatrix} 4\u002F3 & 1 \\\\ 1 & 16\u002F3 \\end{pmatrix}",[571,4436,4438],{"className":4437,"ariaHidden":620},[619],[571,4439,4441,4444],{"className":4440},[624],[571,4442],{"className":4443,"style":2721},[628],[571,4445,4447,4453,4557],{"className":4446},[2725],[571,4448,4450],{"className":4449,"style":2730},[639,2729],[571,4451,597],{"className":4452},[2734,916],[571,4454,4456],{"className":4455},[633],[571,4457,4459,4505,4508,4511],{"className":4458},[2542],[571,4460,4462],{"className":4461},[2744],[571,4463,4465,4497],{"className":4464},[893,1047],[571,4466,4468,4494],{"className":4467},[897],[571,4469,4471,4483],{"className":4470,"style":2754},[901],[571,4472,4473,4476],{"style":2757},[571,4474],{"className":4475,"style":1361},[909],[571,4477,4479],{"className":4478},[633],[571,4480,4482],{"className":4481},[633],"4\u002F3",[571,4484,4485,4488],{"style":2819},[571,4486],{"className":4487,"style":1361},[909],[571,4489,4491],{"className":4490},[633],[571,4492,1532],{"className":4493},[633],[571,4495,1071],{"className":4496},[1070],[571,4498,4500],{"className":4499},[897],[571,4501,4503],{"className":4502,"style":2888},[901],[571,4504],{},[571,4506],{"className":4507,"style":3065},[3064],[571,4509],{"className":4510,"style":3065},[3064],[571,4512,4514],{"className":4513},[2744],[571,4515,4517,4549],{"className":4516},[893,1047],[571,4518,4520,4546],{"className":4519},[897],[571,4521,4523,4534],{"className":4522,"style":2754},[901],[571,4524,4525,4528],{"style":2757},[571,4526],{"className":4527,"style":1361},[909],[571,4529,4531],{"className":4530},[633],[571,4532,1532],{"className":4533},[633],[571,4535,4536,4539],{"style":2819},[571,4537],{"className":4538,"style":1361},[909],[571,4540,4542],{"className":4541},[633],[571,4543,4545],{"className":4544},[633],"16\u002F3",[571,4547,1071],{"className":4548},[1070],[571,4550,4552],{"className":4551},[897],[571,4553,4555],{"className":4554,"style":2888},[901],[571,4556],{},[571,4558,4560],{"className":4559,"style":2730},[646,2729],[571,4561,603],{"className":4562},[2734,916],". Das System hat die Lösung ",[571,4565,4567,4610],{"className":4566},[574],[571,4568,4570],{"className":4569},[578],[580,4571,4572],{"xmlns":582},[584,4573,4574,4607],{},[587,4575,4576,4578,4580],{},[590,4577,801],{"mathvariant":800},[594,4579,606],{},[587,4581,4582,4584,4592,4594,4596,4598,4605],{},[594,4583,597],{"fence":620},[1297,4585,4586,4589],{},[608,4587,4588],{},"59",[608,4590,4591],{},"165",[594,4593,3255],{"separator":620},[854,4595,3258],{},[594,4597,1551],{},[1297,4599,4600,4603],{},[608,4601,4602],{},"97",[608,4604,4591],{},[594,4606,603],{"fence":620},[612,4608,4609],{"encoding":614},"\\Delta = \\left(\\frac{59}{165};\\ -\\frac{97}{165}\\right)",[571,4611,4613,4631],{"className":4612,"ariaHidden":620},[619],[571,4614,4616,4619,4622,4625,4628],{"className":4615},[624],[571,4617],{"className":4618,"style":755},[628],[571,4620,801],{"className":4621},[633],[571,4623],{"className":4624,"style":651},[650],[571,4626,606],{"className":4627},[655],[571,4629],{"className":4630,"style":651},[650],[571,4632,4634,4637],{"className":4633},[624],[571,4635],{"className":4636,"style":3691},[628],[571,4638,4640,4646,4714,4717,4720,4723,4726,4794],{"className":4639},[2725],[571,4641,4643],{"className":4642,"style":2730},[639,2729],[571,4644,597],{"className":4645},[2734,1402],[571,4647,4649,4652,4711],{"className":4648},[633],[571,4650],{"className":4651},[639,1341],[571,4653,4655],{"className":4654},[1297],[571,4656,4658,4703],{"className":4657},[893,1047],[571,4659,4661,4700],{"className":4660},[897],[571,4662,4664,4678,4686],{"className":4663,"style":3722},[901],[571,4665,4666,4669],{"style":1357},[571,4667],{"className":4668,"style":1361},[909],[571,4670,4672],{"className":4671},[914,915,916,917],[571,4673,4675],{"className":4674},[633,917],[571,4676,4591],{"className":4677},[633,917],[571,4679,4680,4683],{"style":1421},[571,4681],{"className":4682,"style":1361},[909],[571,4684],{"className":4685,"style":1429},[1428],[571,4687,4688,4691],{"style":3747},[571,4689],{"className":4690,"style":1361},[909],[571,4692,4694],{"className":4693},[914,915,916,917],[571,4695,4697],{"className":4696},[633,917],[571,4698,4588],{"className":4699},[633,917],[571,4701,1071],{"className":4702},[1070],[571,4704,4706],{"className":4705},[897],[571,4707,4709],{"className":4708,"style":3769},[901],[571,4710],{},[571,4712],{"className":4713},[646,1341],[571,4715,3255],{"className":4716},[2695],[571,4718,3258],{"className":4719},[650],[571,4721],{"className":4722,"style":1128},[650],[571,4724,1551],{"className":4725},[633],[571,4727,4729,4732,4791],{"className":4728},[633],[571,4730],{"className":4731},[639,1341],[571,4733,4735],{"className":4734},[1297],[571,4736,4738,4783],{"className":4737},[893,1047],[571,4739,4741,4780],{"className":4740},[897],[571,4742,4744,4758,4766],{"className":4743,"style":3722},[901],[571,4745,4746,4749],{"style":1357},[571,4747],{"className":4748,"style":1361},[909],[571,4750,4752],{"className":4751},[914,915,916,917],[571,4753,4755],{"className":4754},[633,917],[571,4756,4591],{"className":4757},[633,917],[571,4759,4760,4763],{"style":1421},[571,4761],{"className":4762,"style":1361},[909],[571,4764],{"className":4765,"style":1429},[1428],[571,4767,4768,4771],{"style":3747},[571,4769],{"className":4770,"style":1361},[909],[571,4772,4774],{"className":4773},[914,915,916,917],[571,4775,4777],{"className":4776},[633,917],[571,4778,4602],{"className":4779},[633,917],[571,4781,1071],{"className":4782},[1070],[571,4784,4786],{"className":4785},[897],[571,4787,4789],{"className":4788,"style":3769},[901],[571,4790],{},[571,4792],{"className":4793},[646,1341],[571,4795,4797],{"className":4796,"style":2730},[646,2729],[571,4798,603],{"className":4799},[2734,1402],", also",[571,4802,4804],{"className":4803},[763],[571,4805,4807,4873],{"className":4806},[574],[571,4808,4810],{"className":4809},[578],[580,4811,4812],{"xmlns":582,"display":772},[584,4813,4814,4870],{},[587,4815,4816,4828,4830,4854,4856,4858,4861,4863,4865,4868],{},[782,4817,4818,4820],{},[590,4819,600],{},[587,4821,4822,4824,4826],{},[594,4823,597],{"stretchy":596},[608,4825,2564],{},[594,4827,603],{"stretchy":596},[594,4829,606],{},[587,4831,4832,4834,4841,4843,4845,4852],{},[594,4833,597],{"fence":620},[1297,4835,4836,4839],{},[608,4837,4838],{},"169",[608,4840,4591],{},[594,4842,3255],{"separator":620},[854,4844,3258],{},[1297,4846,4847,4850],{},[608,4848,4849],{},"343",[608,4851,4591],{},[594,4853,603],{"fence":620},[594,4855,808],{},[594,4857,597],{"stretchy":596},[608,4859,4860],{},"1,0242",[594,4862,3255],{"separator":620},[854,4864,3258],{},[608,4866,4867],{},"2,0788",[594,4869,603],{"stretchy":596},[612,4871,4872],{"encoding":614},"x^{(2)} = \\left(\\frac{169}{165};\\ \\frac{343}{165}\\right) \\approx (1{,}0242;\\ 2{,}0788)",[571,4874,4876,4929,5096],{"className":4875,"ariaHidden":620},[619],[571,4877,4879,4882,4920,4923,4926],{"className":4878},[624],[571,4880],{"className":4881,"style":902},[628],[571,4883,4885,4888],{"className":4884},[633],[571,4886,600],{"className":4887},[633,634],[571,4889,4891],{"className":4890},[889],[571,4892,4894],{"className":4893},[893],[571,4895,4897],{"className":4896},[897],[571,4898,4900],{"className":4899,"style":902},[901],[571,4901,4902,4905],{"style":905},[571,4903],{"className":4904,"style":910},[909],[571,4906,4908],{"className":4907},[914,915,916,917],[571,4909,4911,4914,4917],{"className":4910},[633,917],[571,4912,597],{"className":4913},[639,917],[571,4915,2564],{"className":4916},[633,917],[571,4918,603],{"className":4919},[646,917],[571,4921],{"className":4922,"style":651},[650],[571,4924,606],{"className":4925},[655],[571,4927],{"className":4928,"style":651},[650],[571,4930,4932,4935,5087,5090,5093],{"className":4931},[624],[571,4933],{"className":4934,"style":2721},[628],[571,4936,4938,4944,5010,5013,5016,5019,5081],{"className":4937},[2725],[571,4939,4941],{"className":4940,"style":2730},[639,2729],[571,4942,597],{"className":4943},[2734,916],[571,4945,4947,4950,5007],{"className":4946},[633],[571,4948],{"className":4949},[639,1341],[571,4951,4953],{"className":4952},[1297],[571,4954,4956,4998],{"className":4955},[893,1047],[571,4957,4959,4995],{"className":4958},[897],[571,4960,4963,4975,4983],{"className":4961,"style":4962},[901],"height:1.3214em;",[571,4964,4966,4969],{"style":4965},"top:-2.314em;",[571,4967],{"className":4968,"style":1361},[909],[571,4970,4972],{"className":4971},[633],[571,4973,4591],{"className":4974},[633],[571,4976,4977,4980],{"style":1421},[571,4978],{"className":4979,"style":1361},[909],[571,4981],{"className":4982,"style":1429},[1428],[571,4984,4986,4989],{"style":4985},"top:-3.677em;",[571,4987],{"className":4988,"style":1361},[909],[571,4990,4992],{"className":4991},[633],[571,4993,4838],{"className":4994},[633],[571,4996,1071],{"className":4997},[1070],[571,4999,5001],{"className":5000},[897],[571,5002,5005],{"className":5003,"style":5004},[901],"height:0.686em;",[571,5006],{},[571,5008],{"className":5009},[646,1341],[571,5011,3255],{"className":5012},[2695],[571,5014,3258],{"className":5015},[650],[571,5017],{"className":5018,"style":1128},[650],[571,5020,5022,5025,5078],{"className":5021},[633],[571,5023],{"className":5024},[639,1341],[571,5026,5028],{"className":5027},[1297],[571,5029,5031,5070],{"className":5030},[893,1047],[571,5032,5034,5067],{"className":5033},[897],[571,5035,5037,5048,5056],{"className":5036,"style":4962},[901],[571,5038,5039,5042],{"style":4965},[571,5040],{"className":5041,"style":1361},[909],[571,5043,5045],{"className":5044},[633],[571,5046,4591],{"className":5047},[633],[571,5049,5050,5053],{"style":1421},[571,5051],{"className":5052,"style":1361},[909],[571,5054],{"className":5055,"style":1429},[1428],[571,5057,5058,5061],{"style":4985},[571,5059],{"className":5060,"style":1361},[909],[571,5062,5064],{"className":5063},[633],[571,5065,4849],{"className":5066},[633],[571,5068,1071],{"className":5069},[1070],[571,5071,5073],{"className":5072},[897],[571,5074,5076],{"className":5075,"style":5004},[901],[571,5077],{},[571,5079],{"className":5080},[646,1341],[571,5082,5084],{"className":5083,"style":2730},[646,2729],[571,5085,603],{"className":5086},[2734,916],[571,5088],{"className":5089,"style":651},[650],[571,5091,808],{"className":5092},[655],[571,5094],{"className":5095,"style":651},[650],[571,5097,5099,5102,5105,5108,5114,5118,5121,5124,5127,5130,5136,5140],{"className":5098},[624],[571,5100],{"className":5101,"style":629},[628],[571,5103,597],{"className":5104},[639],[571,5106,1532],{"className":5107},[633],[571,5109,5111],{"className":5110},[633],[571,5112,2529],{"className":5113},[2695],[571,5115,5117],{"className":5116},[633],"0242",[571,5119,3255],{"className":5120},[2695],[571,5122,3258],{"className":5123},[650],[571,5125],{"className":5126,"style":1128},[650],[571,5128,2564],{"className":5129},[633],[571,5131,5133],{"className":5132},[633],[571,5134,2529],{"className":5135},[2695],[571,5137,5139],{"className":5138},[633],"0788",[571,5141,603],{"className":5142},[646],[563,5144,5145,5146,5187,5188,5217,5218,5258,5259,5356],{},"Der größte Komponentenfehler ist ",[571,5147,5149,5164],{"className":5148},[574],[571,5150,5152],{"className":5151},[578],[580,5153,5154],{"xmlns":582},[584,5155,5156,5161],{},[587,5157,5158],{},[608,5159,5160],{},"0,079",[612,5162,5163],{"encoding":614},"0{,}079",[571,5165,5167],{"className":5166,"ariaHidden":620},[619],[571,5168,5170,5174,5177,5183],{"className":5169},[624],[571,5171],{"className":5172,"style":5173},[628],"height:0.8389em;vertical-align:-0.1944em;",[571,5175,610],{"className":5176},[633],[571,5178,5180],{"className":5179},[633],[571,5181,2529],{"className":5182},[2695],[571,5184,5186],{"className":5185},[633],"079"," (in ",[571,5189,5191,5204],{"className":5190},[574],[571,5192,5194],{"className":5193},[578],[580,5195,5196],{"xmlns":582},[584,5197,5198,5202],{},[587,5199,5200],{},[590,5201,2532],{},[612,5203,2532],{"encoding":614},[571,5205,5207],{"className":5206,"ariaHidden":620},[619],[571,5208,5210,5214],{"className":5209},[624],[571,5211],{"className":5212,"style":5213},[628],"height:0.625em;vertical-align:-0.1944em;",[571,5215,2532],{"className":5216,"style":2702},[633,634],"). Ein weiterer Schritt drückt ihn auf etwa ",[571,5219,5221,5236],{"className":5220},[574],[571,5222,5224],{"className":5223},[578],[580,5225,5226],{"xmlns":582},[584,5227,5228,5233],{},[587,5229,5230],{},[608,5231,5232],{},"0,0016",[612,5234,5235],{"encoding":614},"0{,}0016",[571,5237,5239],{"className":5238,"ariaHidden":620},[619],[571,5240,5242,5245,5248,5254],{"className":5241},[624],[571,5243],{"className":5244,"style":5173},[628],[571,5246,610],{"className":5247},[633],[571,5249,5251],{"className":5250},[633],[571,5252,2529],{"className":5253},[2695],[571,5255,5257],{"className":5256},[633],"0016",", der nächste auf etwa ",[571,5260,5262,5291],{"className":5261},[574],[571,5263,5265],{"className":5264},[578],[580,5266,5267],{"xmlns":582},[584,5268,5269,5288],{},[587,5270,5271,5274,5277],{},[608,5272,5273],{},"7",[594,5275,5276],{},"⋅",[782,5278,5279,5282],{},[608,5280,5281],{},"10",[587,5283,5284,5286],{},[594,5285,1551],{},[608,5287,5273],{},[612,5289,5290],{"encoding":614},"7 \\cdot 10^{-7}",[571,5292,5294,5312],{"className":5293,"ariaHidden":620},[619],[571,5295,5297,5300,5303,5306,5309],{"className":5296},[624],[571,5298],{"className":5299,"style":665},[628],[571,5301,5273],{"className":5302},[633],[571,5304],{"className":5305,"style":934},[650],[571,5307,5276],{"className":5308},[938],[571,5310],{"className":5311,"style":934},[650],[571,5313,5315,5318,5321],{"className":5314},[624],[571,5316],{"className":5317,"style":1826},[628],[571,5319,1532],{"className":5320},[633],[571,5322,5324,5327],{"className":5323},[633],[571,5325,610],{"className":5326},[633],[571,5328,5330],{"className":5329},[889],[571,5331,5333],{"className":5332},[893],[571,5334,5336],{"className":5335},[897],[571,5337,5339],{"className":5338,"style":1826},[901],[571,5340,5341,5344],{"style":1194},[571,5342],{"className":5343,"style":910},[909],[571,5345,5347],{"className":5346},[914,915,916,917],[571,5348,5350,5353],{"className":5349},[633,917],[571,5351,1551],{"className":5352},[633,917],[571,5354,5273],{"className":5355},[633,917],": Die Zahl der richtigen Stellen verdoppelt sich ungefähr.",[558,5358,5360],{"id":5359},"typische-fehler","Typische Fehler",[1976,5362,5363,5550,5656,5659],{},[1979,5364,5365,5366,5460,5461,1502],{},"Das Vorzeichen vergessen: Rechts steht ",[571,5367,5369,5401],{"className":5368},[574],[571,5370,5372],{"className":5371},[578],[580,5373,5374],{"xmlns":582},[584,5375,5376,5398],{},[587,5377,5378,5380,5382,5384,5396],{},[594,5379,1551],{},[590,5381,592],{},[594,5383,597],{"stretchy":596},[782,5385,5386,5388],{},[590,5387,600],{},[587,5389,5390,5392,5394],{},[594,5391,597],{"stretchy":596},[590,5393,792],{},[594,5395,603],{"stretchy":596},[594,5397,603],{"stretchy":596},[612,5399,5400],{"encoding":614},"-F(x^{(k)})",[571,5402,5404],{"className":5403,"ariaHidden":620},[619],[571,5405,5407,5410,5413,5416,5419,5457],{"className":5406},[624],[571,5408],{"className":5409,"style":1726},[628],[571,5411,1551],{"className":5412},[633],[571,5414,592],{"className":5415,"style":635},[633,634],[571,5417,597],{"className":5418},[639],[571,5420,5422,5425],{"className":5421},[633],[571,5423,600],{"className":5424},[633,634],[571,5426,5428],{"className":5427},[889],[571,5429,5431],{"className":5430},[893],[571,5432,5434],{"className":5433},[897],[571,5435,5437],{"className":5436,"style":1612},[901],[571,5438,5439,5442],{"style":1194},[571,5440],{"className":5441,"style":910},[909],[571,5443,5445],{"className":5444},[914,915,916,917],[571,5446,5448,5451,5454],{"className":5447},[633,917],[571,5449,597],{"className":5450},[639,917],[571,5452,792],{"className":5453,"style":927},[633,634,917],[571,5455,603],{"className":5456},[646,917],[571,5458,603],{"className":5459},[646],", nicht ",[571,5462,5464,5494],{"className":5463},[574],[571,5465,5467],{"className":5466},[578],[580,5468,5469],{"xmlns":582},[584,5470,5471,5491],{},[587,5472,5473,5475,5477,5489],{},[590,5474,592],{},[594,5476,597],{"stretchy":596},[782,5478,5479,5481],{},[590,5480,600],{},[587,5482,5483,5485,5487],{},[594,5484,597],{"stretchy":596},[590,5486,792],{},[594,5488,603],{"stretchy":596},[594,5490,603],{"stretchy":596},[612,5492,5493],{"encoding":614},"F(x^{(k)})",[571,5495,5497],{"className":5496,"ariaHidden":620},[619],[571,5498,5500,5503,5506,5509,5547],{"className":5499},[624],[571,5501],{"className":5502,"style":1726},[628],[571,5504,592],{"className":5505,"style":635},[633,634],[571,5507,597],{"className":5508},[639],[571,5510,5512,5515],{"className":5511},[633],[571,5513,600],{"className":5514},[633,634],[571,5516,5518],{"className":5517},[889],[571,5519,5521],{"className":5520},[893],[571,5522,5524],{"className":5523},[897],[571,5525,5527],{"className":5526,"style":1612},[901],[571,5528,5529,5532],{"style":1194},[571,5530],{"className":5531,"style":910},[909],[571,5533,5535],{"className":5534},[914,915,916,917],[571,5536,5538,5541,5544],{"className":5537},[633,917],[571,5539,597],{"className":5540},[639,917],[571,5542,792],{"className":5543,"style":927},[633,634,917],[571,5545,603],{"className":5546},[646,917],[571,5548,603],{"className":5549},[646],[1979,5551,5552,5553,5582,5583,5655],{},"Zeilen und Spalten der Jacobi-Matrix vertauschen. Zeile ",[571,5554,5556,5569],{"className":5555},[574],[571,5557,5559],{"className":5558},[578],[580,5560,5561],{"xmlns":582},[584,5562,5563,5567],{},[587,5564,5565],{},[590,5566,1310],{},[612,5568,1310],{"encoding":614},[571,5570,5572],{"className":5571,"ariaHidden":620},[619],[571,5573,5575,5579],{"className":5574},[624],[571,5576],{"className":5577,"style":5578},[628],"height:0.6595em;",[571,5580,1310],{"className":5581},[633,634]," enthält die Ableitungen von ",[571,5584,5586,5604],{"className":5585},[574],[571,5587,5589],{"className":5588},[578],[580,5590,5591],{"xmlns":582},[584,5592,5593,5601],{},[587,5594,5595],{},[830,5596,5597,5599],{},[590,5598,592],{},[590,5600,1310],{},[612,5602,5603],{"encoding":614},"F_i",[571,5605,5607],{"className":5606,"ariaHidden":620},[619],[571,5608,5610,5613],{"className":5609},[624],[571,5611],{"className":5612,"style":1242},[628],[571,5614,5616,5619],{"className":5615},[633],[571,5617,592],{"className":5618,"style":635},[633,634],[571,5620,5622],{"className":5621},[889],[571,5623,5625,5647],{"className":5624},[893,1047],[571,5626,5628,5644],{"className":5627},[897],[571,5629,5632],{"className":5630,"style":5631},[901],"height:0.3117em;",[571,5633,5635,5638],{"style":5634},"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;",[571,5636],{"className":5637,"style":910},[909],[571,5639,5641],{"className":5640},[914,915,916,917],[571,5642,1310],{"className":5643},[633,634,917],[571,5645,1071],{"className":5646},[1070],[571,5648,5650],{"className":5649},[897],[571,5651,5653],{"className":5652,"style":1078},[901],[571,5654],{}," nach allen Variablen.",[1979,5657,5658],{},"Die Inverse der Jacobi-Matrix explizit berechnen. Das ist teurer und numerisch ungünstiger als das Lösen des Systems.",[1979,5660,5661],{},"Bei einer (fast) singulären Jacobi-Matrix weiterrechnen. Dann ist der Schritt nicht oder nur ungenau bestimmt.",{"title":5663,"searchDepth":5664,"depth":5664,"links":5665},"",2,[5666,5667,5668],{"id":560,"depth":5664,"text":561},{"id":2501,"depth":5664,"text":2502},{"id":5359,"depth":5664,"text":5360},[5670,5672,5674,5676,5678,5680,5683,5686,5689,5692,5695,5698,5701,5704,5707],{"lhs":5671,"rhs":610},"1^2 + 2 - 3",{"lhs":5673,"rhs":610},"1 + 2^2 - 5",{"lhs":5675,"rhs":1532},"2*(-1\u002F3) + 5\u002F3",{"lhs":5677,"rhs":2573},"-1\u002F3 + 2*5\u002F3",{"lhs":5679,"rhs":2573},"det([[2, 1], [1, 2]])",{"lhs":5681,"rhs":5682},"(2\u002F3)^2 + 8\u002F3 - 3","1\u002F9",{"lhs":5684,"rhs":5685},"2\u002F3 + (8\u002F3)^2 - 5","25\u002F9",{"lhs":5687,"rhs":5688},"4\u002F3*59\u002F165 + (-97\u002F165)","-1\u002F9",{"lhs":5690,"rhs":5691},"59\u002F165 + 16\u002F3*(-97\u002F165)","-25\u002F9",{"lhs":5693,"rhs":5694},"2\u002F3 + 59\u002F165","169\u002F165",{"lhs":5696,"rhs":5697},"8\u002F3 - 97\u002F165","343\u002F165",{"lhs":5699,"rhs":5700},"round(169\u002F165, 4)","1.0242",{"lhs":5702,"rhs":5703},"round(343\u002F165, 4)","2.0788",{"lhs":5705,"rhs":5706},"round(343\u002F165 - 2, 3)","0.079",{"lhs":5708,"rhs":5709},"round(343\u002F165 + inv([[2*169\u002F165, 1], [1, 2*343\u002F165]])[2, 1]*(-((169\u002F165)^2 + 343\u002F165 - 3)) + inv([[2*169\u002F165, 1], [1, 2*343\u002F165]])[2, 2]*(-(169\u002F165 + (343\u002F165)^2 - 5)) - 2, 4)","0.0016","F: \\mathbb{R}^n \\to \\mathbb{R}^n \\text{ stetig differenzierbar},\\ J_F(x^{(k)}) \\text{ invertierbar}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>F\u003C\u002Fmi>\u003Cmo>:\u003C\u002Fmo>\u003Cmsup>\u003Cmi mathvariant=\"double-struck\">R\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsup>\u003Cmo>→\u003C\u002Fmo>\u003Cmsup>\u003Cmi mathvariant=\"double-struck\">R\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">F: \\mathbb{R}^n \\to \\mathbb{R}^n\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">:\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6889em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathbb\">R\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6644em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">→\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6889em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathbb\">R\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6644em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">stetig\u003C\u002Fspan> \u003Cspan style=\"white-space: nowrap\">\u003Cspan class=\"katex\">differenzierbar\u003C\u002Fspan>\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.3em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>J\u003C\u002Fmi>\u003Cmi>F\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmsup>\u003Cmi>x\u003C\u002Fmi>\u003Cmrow>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>k\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">J_F(x^{(k)})\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.138em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0962em;\">J\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3283em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0962em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.1389em;\">F\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.888em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mopen mtight\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"mclose mtight\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">invertierbar\u003C\u002Fspan>",null,"md","newton-method-systems","J_F(x^{(k)})\\,\\Delta x^{(k)} = -F(x^{(k)}), \\qquad x^{(k+1)} = x^{(k)} + \\Delta x^{(k)}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>J\u003C\u002Fmi>\u003Cmi>F\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmsup>\u003Cmi>x\u003C\u002Fmi>\u003Cmrow>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>k\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi mathvariant=\"normal\">Δ\u003C\u002Fmi>\u003Cmsup>\u003Cmi>x\u003C\u002Fmi>\u003Cmrow>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>k\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003Cmo>=\u003C\u002Fmo>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>F\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmsup>\u003Cmi>x\u003C\u002Fmi>\u003Cmrow>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>k\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"2em\"\u002F>\u003Cmsup>\u003Cmi>x\u003C\u002Fmi>\u003Cmrow>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>k\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003Cmo>=\u003C\u002Fmo>\u003Cmsup>\u003Cmi>x\u003C\u002Fmi>\u003Cmrow>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>k\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003Cmo>+\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">Δ\u003C\u002Fmi>\u003Cmsup>\u003Cmi>x\u003C\u002Fmi>\u003Cmrow>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>k\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">J_F(x^{(k)})\\,\\Delta x^{(k)} = -F(x^{(k)}), \\qquad x^{(k+1)} = x^{(k)} + \\Delta x^{(k)}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.188em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0962em;\">J\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3283em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0962em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.1389em;\">F\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.938em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mopen mtight\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"mclose mtight\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">Δ\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.938em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mopen mtight\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"mclose mtight\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.188em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">−\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.938em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mopen mtight\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"mclose mtight\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:2em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.938em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mopen mtight\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"mbin mtight\">+\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003Cspan class=\"mclose mtight\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.0213em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.938em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mopen mtight\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"mclose mtight\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.938em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">Δ\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.938em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mopen mtight\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"mclose mtight\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fnumerics\u002Fnewton-verfahren-gleichungssysteme",[],[5723,5724,5725,5726],"newton-method","order-of-convergence","lu-decomposition","jacobian-matrix",{"title":548,"description":5663},"de\u002Fformulas\u002Fmath\u002Fnumerics\u002Fnewton-verfahren-gleichungssysteme","Das Newton-Verfahren für Systeme ersetzt F durch seine Linearisierung und löst in jedem Schritt ein lineares Gleichungssystem.",[5731,5732,5733,5734],"nichtlineares gleichungssystem","newton-verfahren","jacobi-matrix","iterationsverfahren",[5736,5739,5743,5746],{"symbol":592,"meaning":5737,"symbolHtml":5738},"Funktion, deren Nullstelle F(x) = 0 gesucht ist","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>F\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">F\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":5740,"meaning":5741,"symbolHtml":5742},"x^{(k)}","Näherungsvektor nach k Schritten","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsup>\u003Cmi>x\u003C\u002Fmi>\u003Cmrow>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>k\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x^{(k)}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.888em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.888em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mopen mtight\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"mclose mtight\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":1232,"meaning":5744,"symbolHtml":5745},"Jacobi-Matrix von F, Matrix der partiellen Ableitungen ∂F_i\u002F∂x_j","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>J\u003C\u002Fmi>\u003Cmi>F\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">J_F\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8333em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0962em;\">J\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3283em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0962em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.1389em;\">F\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":1920,"meaning":5747,"symbolHtml":5748},"Korrekturvektor im k-ten Schritt","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi mathvariant=\"normal\">Δ\u003C\u002Fmi>\u003Cmsup>\u003Cmi>x\u003C\u002Fmi>\u003Cmrow>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>k\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\Delta x^{(k)}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.888em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">Δ\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.888em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mopen mtight\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"mclose mtight\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","tfq3ddA7rJ_kCEfTPo69-nPiYH-PHv1oIKyFiezJ7r8",[5751,5753,5756,5759],{"stem":5752,"title":1210,"category":368},"de\u002Fformulas\u002Fmath\u002Fmultivariable-calculus\u002Fjacobi-matrix",{"stem":5754,"title":5755,"category":391},"de\u002Fformulas\u002Fmath\u002Fnumerics\u002Fkonvergenzordnung","Konvergenzordnung",{"stem":5757,"title":5758,"category":391},"de\u002Fformulas\u002Fmath\u002Fnumerics\u002Flu-zerlegung","LU-Zerlegung",{"stem":5760,"title":5761,"category":391},"de\u002Fformulas\u002Fmath\u002Fnumerics\u002Fnewton-verfahren","Newton-Verfahren",1793824266211]