[{"data":1,"prerenderedAt":3473},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Fnumerics\u002Fjacobi-verfahren":546,"formula-related-de\u002Fformulas\u002Fmath\u002Fnumerics\u002Fjacobi-verfahren":3460},[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":3375,"conditions":3413,"conditionsHtml":3414,"deprecated":3415,"description":3369,"extension":3416,"figure":3415,"figureCaption":3415,"figureHtml":3415,"formulaId":3417,"latex":3418,"latexHtml":3419,"level":3420,"meta":3421,"navigation":3422,"path":3423,"redirectFrom":3424,"related":3425,"seo":3430,"stem":3431,"subject":583,"summary":3432,"tags":3433,"variables":3438,"__hash__":3459},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Fnumerics\u002Fjacobi-verfahren.md","Jacobi-Verfahren",[550,551,552,553],"Gesamtschrittverfahren","Jacobi-Iteration","Jacobiverfahren","iterative Lösung lineares Gleichungssystem",{"type":555,"value":556,"toc":3368},"minimark",[557,562,776,884,1188,1191,1446,1449,1453,1456,1780,2074,2643,2768,3042,3236,3240],[558,559,561],"h2",{"id":560},"erklärung","Erklärung",[563,564,565,566,569,570,572,573,655,656,686,687,775],"p",{},"Das ",[567,568,548],"strong",{}," (auch ",[567,571,550],{},") löst ein lineares Gleichungssystem ",[574,575,578,611],"span",{"className":576},[577],"katex",[574,579,582],{"className":580},[581],"katex-mathml",[583,584,586],"math",{"xmlns":585},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[587,588,589,606],"semantics",{},[590,591,592,596,599,603],"mrow",{},[593,594,595],"mi",{},"A",[593,597,598],{},"x",[600,601,602],"mo",{},"=",[593,604,605],{},"b",[607,608,610],"annotation",{"encoding":609},"application\u002Fx-tex","Ax = b",[574,612,616,645],{"className":613,"ariaHidden":615},[614],"katex-html","true",[574,617,620,625,630,633,638,642],{"className":618},[619],"base",[574,621],{"className":622,"style":624},[623],"strut","height:0.6833em;",[574,626,595],{"className":627},[628,629],"mord","mathnormal",[574,631,598],{"className":632},[628,629],[574,634],{"className":635,"style":637},[636],"mspace","margin-right:0.2778em;",[574,639,602],{"className":640},[641],"mrel",[574,643],{"className":644,"style":637},[636],[574,646,648,652],{"className":647},[619],[574,649],{"className":650,"style":651},[623],"height:0.6944em;",[574,653,605],{"className":654},[628,629]," iterativ. Man löst die ",[574,657,659,673],{"className":658},[577],[574,660,662],{"className":661},[581],[583,663,664],{"xmlns":585},[587,665,666,671],{},[590,667,668],{},[593,669,670],{},"i",[607,672,670],{"encoding":609},[574,674,676],{"className":675,"ariaHidden":615},[614],[574,677,679,683],{"className":678},[619],[574,680],{"className":681,"style":682},[623],"height:0.6595em;",[574,684,670],{"className":685},[628,629],"-te Gleichung nach ",[574,688,690,709],{"className":689},[577],[574,691,693],{"className":692},[581],[583,694,695],{"xmlns":585},[587,696,697,706],{},[590,698,699],{},[700,701,702,704],"msub",{},[593,703,598],{},[593,705,670],{},[607,707,708],{"encoding":609},"x_i",[574,710,712],{"className":711,"ariaHidden":615},[614],[574,713,715,719],{"className":714},[619],[574,716],{"className":717,"style":718},[623],"height:0.5806em;vertical-align:-0.15em;",[574,720,722,725],{"className":721},[628],[574,723,598],{"className":724},[628,629],[574,726,729],{"className":727},[728],"msupsub",[574,730,734,766],{"className":731},[732,733],"vlist-t","vlist-t2",[574,735,738,761],{"className":736},[737],"vlist-r",[574,739,743],{"className":740,"style":742},[741],"vlist","height:0.3117em;",[574,744,746,751],{"style":745},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[574,747],{"className":748,"style":750},[749],"pstrut","height:2.7em;",[574,752,758],{"className":753},[754,755,756,757],"sizing","reset-size6","size3","mtight",[574,759,670],{"className":760},[628,629,757],[574,762,765],{"className":763},[764],"vlist-s","​",[574,767,769],{"className":768},[737],[574,770,773],{"className":771,"style":772},[741],"height:0.15em;",[574,774],{}," auf und setzt rechts die Werte aus dem vorigen Schritt ein. Alle Komponenten des neuen Vektors werden also gleichzeitig aus dem alten berechnet.",[563,777,778,779,883],{},"In Matrixform mit ",[574,780,782,812],{"className":781},[577],[574,783,785],{"className":784},[581],[583,786,787],{"xmlns":585},[587,788,789,809],{},[590,790,791,793,795,798,801,804,806],{},[593,792,595],{},[600,794,602],{},[593,796,797],{},"D",[600,799,800],{},"+",[593,802,803],{},"L",[600,805,800],{},[593,807,808],{},"R",[607,810,811],{"encoding":609},"A = D + L + R",[574,813,815,833,855,873],{"className":814,"ariaHidden":615},[614],[574,816,818,821,824,827,830],{"className":817},[619],[574,819],{"className":820,"style":624},[623],[574,822,595],{"className":823},[628,629],[574,825],{"className":826,"style":637},[636],[574,828,602],{"className":829},[641],[574,831],{"className":832,"style":637},[636],[574,834,836,840,844,848,852],{"className":835},[619],[574,837],{"className":838,"style":839},[623],"height:0.7667em;vertical-align:-0.0833em;",[574,841,797],{"className":842,"style":843},[628,629],"margin-right:0.0278em;",[574,845],{"className":846,"style":847},[636],"margin-right:0.2222em;",[574,849,800],{"className":850},[851],"mbin",[574,853],{"className":854,"style":847},[636],[574,856,858,861,864,867,870],{"className":857},[619],[574,859],{"className":860,"style":839},[623],[574,862,803],{"className":863},[628,629],[574,865],{"className":866,"style":847},[636],[574,868,800],{"className":869},[851],[574,871],{"className":872,"style":847},[636],[574,874,876,879],{"className":875},[619],[574,877],{"className":878,"style":624},[623],[574,880,808],{"className":881,"style":882},[628,629],"margin-right:0.0077em;"," (Diagonale, strikt unteres und strikt oberes Dreieck) lautet ein Schritt",[574,885,888],{"className":886},[887],"katex-display",[574,889,891,975],{"className":890},[577],[574,892,894],{"className":893},[581],[583,895,897],{"xmlns":585,"display":896},"block",[587,898,899,972],{},[590,900,901,924,926,937,940,942,944,946,948,950,952,954,958,970],{},[902,903,904,906],"msup",{},[593,905,598],{},[590,907,908,912,915,917,921],{},[600,909,911],{"stretchy":910},"false","(",[593,913,914],{},"k",[600,916,800],{},[918,919,920],"mn",{},"1",[600,922,923],{"stretchy":910},")",[600,925,602],{},[902,927,928,930],{},[593,929,797],{},[590,931,932,935],{},[600,933,934],{},"−",[918,936,920],{},[600,938,911],{"fence":615,"stretchy":615,"minsize":939,"maxsize":939},"1.2em",[593,941,605],{},[600,943,934],{},[600,945,911],{"stretchy":910},[593,947,803],{},[600,949,800],{},[593,951,808],{},[600,953,923],{"stretchy":910},[955,956,957],"mtext",{}," ",[902,959,960,962],{},[593,961,598],{},[590,963,964,966,968],{},[600,965,911],{"stretchy":910},[593,967,914],{},[600,969,923],{"stretchy":910},[600,971,923],{"fence":615,"stretchy":615,"minsize":939,"maxsize":939},[607,973,974],{"encoding":609},"x^{(k+1)} = D^{-1} \\bigl( b - (L + R)\\,x^{(k)} \\bigr)",[574,976,978,1042,1105,1127],{"className":977,"ariaHidden":615},[614],[574,979,981,985,1033,1036,1039],{"className":980},[619],[574,982],{"className":983,"style":984},[623],"height:0.938em;",[574,986,988,991],{"className":987},[628],[574,989,598],{"className":990},[628,629],[574,992,994],{"className":993},[728],[574,995,997],{"className":996},[732],[574,998,1000],{"className":999},[737],[574,1001,1003],{"className":1002,"style":984},[741],[574,1004,1006,1009],{"style":1005},"top:-3.113em;margin-right:0.05em;",[574,1007],{"className":1008,"style":750},[749],[574,1010,1012],{"className":1011},[754,755,756,757],[574,1013,1015,1019,1023,1026,1029],{"className":1014},[628,757],[574,1016,911],{"className":1017},[1018,757],"mopen",[574,1020,914],{"className":1021,"style":1022},[628,629,757],"margin-right:0.0315em;",[574,1024,800],{"className":1025},[851,757],[574,1027,920],{"className":1028},[628,757],[574,1030,923],{"className":1031},[1032,757],"mclose",[574,1034],{"className":1035,"style":637},[636],[574,1037,602],{"className":1038},[641],[574,1040],{"className":1041,"style":637},[636],[574,1043,1045,1049,1085,1093,1096,1099,1102],{"className":1044},[619],[574,1046],{"className":1047,"style":1048},[623],"height:1.2141em;vertical-align:-0.35em;",[574,1050,1052,1055],{"className":1051},[628],[574,1053,797],{"className":1054,"style":843},[628,629],[574,1056,1058],{"className":1057},[728],[574,1059,1061],{"className":1060},[732],[574,1062,1064],{"className":1063},[737],[574,1065,1068],{"className":1066,"style":1067},[741],"height:0.8641em;",[574,1069,1070,1073],{"style":1005},[574,1071],{"className":1072,"style":750},[749],[574,1074,1076],{"className":1075},[754,755,756,757],[574,1077,1079,1082],{"className":1078},[628,757],[574,1080,934],{"className":1081},[628,757],[574,1083,920],{"className":1084},[628,757],[574,1086,1088],{"className":1087},[1018],[574,1089,911],{"className":1090},[1091,1092],"delimsizing","size1",[574,1094,605],{"className":1095},[628,629],[574,1097],{"className":1098,"style":847},[636],[574,1100,934],{"className":1101},[851],[574,1103],{"className":1104,"style":847},[636],[574,1106,1108,1112,1115,1118,1121,1124],{"className":1107},[619],[574,1109],{"className":1110,"style":1111},[623],"height:1em;vertical-align:-0.25em;",[574,1113,911],{"className":1114},[1018],[574,1116,803],{"className":1117},[628,629],[574,1119],{"className":1120,"style":847},[636],[574,1122,800],{"className":1123},[851],[574,1125],{"className":1126,"style":847},[636],[574,1128,1130,1134,1137,1140,1144,1182],{"className":1129},[619],[574,1131],{"className":1132,"style":1133},[623],"height:1.288em;vertical-align:-0.35em;",[574,1135,808],{"className":1136,"style":882},[628,629],[574,1138,923],{"className":1139},[1032],[574,1141],{"className":1142,"style":1143},[636],"margin-right:0.1667em;",[574,1145,1147,1150],{"className":1146},[628],[574,1148,598],{"className":1149},[628,629],[574,1151,1153],{"className":1152},[728],[574,1154,1156],{"className":1155},[732],[574,1157,1159],{"className":1158},[737],[574,1160,1162],{"className":1161,"style":984},[741],[574,1163,1164,1167],{"style":1005},[574,1165],{"className":1166,"style":750},[749],[574,1168,1170],{"className":1169},[754,755,756,757],[574,1171,1173,1176,1179],{"className":1172},[628,757],[574,1174,911],{"className":1175},[1018,757],[574,1177,914],{"className":1178,"style":1022},[628,629,757],[574,1180,923],{"className":1181},[1032,757],[574,1183,1185],{"className":1184},[1032],[574,1186,923],{"className":1187},[1091,1092],[563,1189,1190],{},"Konvergenz:",[1192,1193,1194,1347],"ul",{},[1195,1196,1197,1198,1201,1202,1316,1317,1346],"li",{},"Das Verfahren konvergiert für jeden Startwert genau dann, wenn der ",[567,1199,1200],{},"Spektralradius"," der Iterationsmatrix ",[574,1203,1205,1239],{"className":1204},[577],[574,1206,1208],{"className":1207},[581],[583,1209,1210],{"xmlns":585},[587,1211,1212,1236],{},[590,1213,1214,1216,1226,1228,1230,1232,1234],{},[600,1215,934],{},[902,1217,1218,1220],{},[593,1219,797],{},[590,1221,1222,1224],{},[600,1223,934],{},[918,1225,920],{},[600,1227,911],{"stretchy":910},[593,1229,803],{},[600,1231,800],{},[593,1233,808],{},[600,1235,923],{"stretchy":910},[607,1237,1238],{"encoding":609},"-D^{-1}(L + R)",[574,1240,1242,1304],{"className":1241,"ariaHidden":615},[614],[574,1243,1245,1249,1252,1289,1292,1295,1298,1301],{"className":1244},[619],[574,1246],{"className":1247,"style":1248},[623],"height:1.0641em;vertical-align:-0.25em;",[574,1250,934],{"className":1251},[628],[574,1253,1255,1258],{"className":1254},[628],[574,1256,797],{"className":1257,"style":843},[628,629],[574,1259,1261],{"className":1260},[728],[574,1262,1264],{"className":1263},[732],[574,1265,1267],{"className":1266},[737],[574,1268,1271],{"className":1269,"style":1270},[741],"height:0.8141em;",[574,1272,1274,1277],{"style":1273},"top:-3.063em;margin-right:0.05em;",[574,1275],{"className":1276,"style":750},[749],[574,1278,1280],{"className":1279},[754,755,756,757],[574,1281,1283,1286],{"className":1282},[628,757],[574,1284,934],{"className":1285},[628,757],[574,1287,920],{"className":1288},[628,757],[574,1290,911],{"className":1291},[1018],[574,1293,803],{"className":1294},[628,629],[574,1296],{"className":1297,"style":847},[636],[574,1299,800],{"className":1300},[851],[574,1302],{"className":1303,"style":847},[636],[574,1305,1307,1310,1313],{"className":1306},[619],[574,1308],{"className":1309,"style":1111},[623],[574,1311,808],{"className":1312,"style":882},[628,629],[574,1314,923],{"className":1315},[1032]," kleiner als ",[574,1318,1320,1333],{"className":1319},[577],[574,1321,1323],{"className":1322},[581],[583,1324,1325],{"xmlns":585},[587,1326,1327,1331],{},[590,1328,1329],{},[918,1330,920],{},[607,1332,920],{"encoding":609},[574,1334,1336],{"className":1335,"ariaHidden":615},[614],[574,1337,1339,1343],{"className":1338},[619],[574,1340],{"className":1341,"style":1342},[623],"height:0.6444em;",[574,1344,920],{"className":1345},[628]," ist. Er bestimmt auch, wie schnell der Fehler schrumpft.",[1195,1348,1349,1350,1353,1354,1445],{},"Hinreichend und leicht zu prüfen ist ",[567,1351,1352],{},"strikte Diagonaldominanz",": In jeder Zeile ist ",[574,1355,1357,1386],{"className":1356},[577],[574,1358,1360],{"className":1359},[581],[583,1361,1362],{"xmlns":585},[587,1363,1364,1383],{},[590,1365,1366,1370,1381],{},[593,1367,1369],{"mathvariant":1368},"normal","∣",[700,1371,1372,1375],{},[593,1373,1374],{},"a",[590,1376,1377,1379],{},[593,1378,670],{},[593,1380,670],{},[593,1382,1369],{"mathvariant":1368},[607,1384,1385],{"encoding":609},"|a_{ii}|",[574,1387,1389],{"className":1388,"ariaHidden":615},[614],[574,1390,1392,1395,1398,1442],{"className":1391},[619],[574,1393],{"className":1394,"style":1111},[623],[574,1396,1369],{"className":1397},[628],[574,1399,1401,1404],{"className":1400},[628],[574,1402,1374],{"className":1403},[628,629],[574,1405,1407],{"className":1406},[728],[574,1408,1410,1434],{"className":1409},[732,733],[574,1411,1413,1431],{"className":1412},[737],[574,1414,1416],{"className":1415,"style":742},[741],[574,1417,1418,1421],{"style":745},[574,1419],{"className":1420,"style":750},[749],[574,1422,1424],{"className":1423},[754,755,756,757],[574,1425,1427],{"className":1426},[628,757],[574,1428,1430],{"className":1429},[628,629,757],"ii",[574,1432,765],{"className":1433},[764],[574,1435,1437],{"className":1436},[737],[574,1438,1440],{"className":1439,"style":772},[741],[574,1441],{},[574,1443,1369],{"className":1444},[628]," größer als die Summe der Beträge der übrigen Einträge.",[563,1447,1448],{},"Iterative Verfahren lohnen sich vor allem bei großen, dünn besetzten Matrizen, bei denen das Gauß-Verfahren zu viel Speicher und Rechenzeit braucht. Da jede Komponente unabhängig berechnet wird, lässt sich das Jacobi-Verfahren gut parallelisieren.",[558,1450,1452],{"id":1451},"beispiele","Beispiele",[563,1454,1455],{},"Das System",[574,1457,1459],{"className":1458},[887],[574,1460,1462,1525],{"className":1461},[577],[574,1463,1465],{"className":1464},[581],[583,1466,1467],{"xmlns":585,"display":896},[587,1468,1469,1522],{},[590,1470,1471,1474,1480,1482,1489,1491,1494,1497,1500,1506,1508,1511,1517,1519],{},[918,1472,1473],{},"4",[700,1475,1476,1478],{},[593,1477,598],{},[918,1479,920],{},[600,1481,800],{},[700,1483,1484,1486],{},[593,1485,598],{},[918,1487,1488],{},"2",[600,1490,602],{},[918,1492,1493],{},"6",[600,1495,1496],{"separator":615},",",[636,1498],{"width":1499},"2em",[700,1501,1502,1504],{},[593,1503,598],{},[918,1505,920],{},[600,1507,800],{},[918,1509,1510],{},"3",[700,1512,1513,1515],{},[593,1514,598],{},[918,1516,1488],{},[600,1518,602],{},[918,1520,1521],{},"7",[607,1523,1524],{"encoding":609},"4x_1 + x_2 = 6, \\qquad x_1 + 3x_2 = 7",[574,1526,1528,1588,1643,1713,1771],{"className":1527,"ariaHidden":615},[614],[574,1529,1531,1535,1538,1579,1582,1585],{"className":1530},[619],[574,1532],{"className":1533,"style":1534},[623],"height:0.7944em;vertical-align:-0.15em;",[574,1536,1473],{"className":1537},[628],[574,1539,1541,1544],{"className":1540},[628],[574,1542,598],{"className":1543},[628,629],[574,1545,1547],{"className":1546},[728],[574,1548,1550,1571],{"className":1549},[732,733],[574,1551,1553,1568],{"className":1552},[737],[574,1554,1557],{"className":1555,"style":1556},[741],"height:0.3011em;",[574,1558,1559,1562],{"style":745},[574,1560],{"className":1561,"style":750},[749],[574,1563,1565],{"className":1564},[754,755,756,757],[574,1566,920],{"className":1567},[628,757],[574,1569,765],{"className":1570},[764],[574,1572,1574],{"className":1573},[737],[574,1575,1577],{"className":1576,"style":772},[741],[574,1578],{},[574,1580],{"className":1581,"style":847},[636],[574,1583,800],{"className":1584},[851],[574,1586],{"className":1587,"style":847},[636],[574,1589,1591,1594,1634,1637,1640],{"className":1590},[619],[574,1592],{"className":1593,"style":718},[623],[574,1595,1597,1600],{"className":1596},[628],[574,1598,598],{"className":1599},[628,629],[574,1601,1603],{"className":1602},[728],[574,1604,1606,1626],{"className":1605},[732,733],[574,1607,1609,1623],{"className":1608},[737],[574,1610,1612],{"className":1611,"style":1556},[741],[574,1613,1614,1617],{"style":745},[574,1615],{"className":1616,"style":750},[749],[574,1618,1620],{"className":1619},[754,755,756,757],[574,1621,1488],{"className":1622},[628,757],[574,1624,765],{"className":1625},[764],[574,1627,1629],{"className":1628},[737],[574,1630,1632],{"className":1631,"style":772},[741],[574,1633],{},[574,1635],{"className":1636,"style":637},[636],[574,1638,602],{"className":1639},[641],[574,1641],{"className":1642,"style":637},[636],[574,1644,1646,1650,1653,1657,1661,1664,1704,1707,1710],{"className":1645},[619],[574,1647],{"className":1648,"style":1649},[623],"height:0.8389em;vertical-align:-0.1944em;",[574,1651,1493],{"className":1652},[628],[574,1654,1496],{"className":1655},[1656],"mpunct",[574,1658],{"className":1659,"style":1660},[636],"margin-right:2em;",[574,1662],{"className":1663,"style":1143},[636],[574,1665,1667,1670],{"className":1666},[628],[574,1668,598],{"className":1669},[628,629],[574,1671,1673],{"className":1672},[728],[574,1674,1676,1696],{"className":1675},[732,733],[574,1677,1679,1693],{"className":1678},[737],[574,1680,1682],{"className":1681,"style":1556},[741],[574,1683,1684,1687],{"style":745},[574,1685],{"className":1686,"style":750},[749],[574,1688,1690],{"className":1689},[754,755,756,757],[574,1691,920],{"className":1692},[628,757],[574,1694,765],{"className":1695},[764],[574,1697,1699],{"className":1698},[737],[574,1700,1702],{"className":1701,"style":772},[741],[574,1703],{},[574,1705],{"className":1706,"style":847},[636],[574,1708,800],{"className":1709},[851],[574,1711],{"className":1712,"style":847},[636],[574,1714,1716,1719,1722,1762,1765,1768],{"className":1715},[619],[574,1717],{"className":1718,"style":1534},[623],[574,1720,1510],{"className":1721},[628],[574,1723,1725,1728],{"className":1724},[628],[574,1726,598],{"className":1727},[628,629],[574,1729,1731],{"className":1730},[728],[574,1732,1734,1754],{"className":1733},[732,733],[574,1735,1737,1751],{"className":1736},[737],[574,1738,1740],{"className":1739,"style":1556},[741],[574,1741,1742,1745],{"style":745},[574,1743],{"className":1744,"style":750},[749],[574,1746,1748],{"className":1747},[754,755,756,757],[574,1749,1488],{"className":1750},[628,757],[574,1752,765],{"className":1753},[764],[574,1755,1757],{"className":1756},[737],[574,1758,1760],{"className":1759,"style":772},[741],[574,1761],{},[574,1763],{"className":1764,"style":637},[636],[574,1766,602],{"className":1767},[641],[574,1769],{"className":1770,"style":637},[636],[574,1772,1774,1777],{"className":1773},[619],[574,1775],{"className":1776,"style":1342},[623],[574,1778,1521],{"className":1779},[628],[563,1781,1782,1783,1875,1876,1968,1969,1875,2022,2073],{},"hat die Lösung ",[574,1784,1786,1808],{"className":1785},[577],[574,1787,1789],{"className":1788},[581],[583,1790,1791],{"xmlns":585},[587,1792,1793,1805],{},[590,1794,1795,1801,1803],{},[700,1796,1797,1799],{},[593,1798,598],{},[918,1800,920],{},[600,1802,602],{},[918,1804,920],{},[607,1806,1807],{"encoding":609},"x_1 = 1",[574,1809,1811,1866],{"className":1810,"ariaHidden":615},[614],[574,1812,1814,1817,1857,1860,1863],{"className":1813},[619],[574,1815],{"className":1816,"style":718},[623],[574,1818,1820,1823],{"className":1819},[628],[574,1821,598],{"className":1822},[628,629],[574,1824,1826],{"className":1825},[728],[574,1827,1829,1849],{"className":1828},[732,733],[574,1830,1832,1846],{"className":1831},[737],[574,1833,1835],{"className":1834,"style":1556},[741],[574,1836,1837,1840],{"style":745},[574,1838],{"className":1839,"style":750},[749],[574,1841,1843],{"className":1842},[754,755,756,757],[574,1844,920],{"className":1845},[628,757],[574,1847,765],{"className":1848},[764],[574,1850,1852],{"className":1851},[737],[574,1853,1855],{"className":1854,"style":772},[741],[574,1856],{},[574,1858],{"className":1859,"style":637},[636],[574,1861,602],{"className":1862},[641],[574,1864],{"className":1865,"style":637},[636],[574,1867,1869,1872],{"className":1868},[619],[574,1870],{"className":1871,"style":1342},[623],[574,1873,920],{"className":1874},[628],", ",[574,1877,1879,1901],{"className":1878},[577],[574,1880,1882],{"className":1881},[581],[583,1883,1884],{"xmlns":585},[587,1885,1886,1898],{},[590,1887,1888,1894,1896],{},[700,1889,1890,1892],{},[593,1891,598],{},[918,1893,1488],{},[600,1895,602],{},[918,1897,1488],{},[607,1899,1900],{"encoding":609},"x_2 = 2",[574,1902,1904,1959],{"className":1903,"ariaHidden":615},[614],[574,1905,1907,1910,1950,1953,1956],{"className":1906},[619],[574,1908],{"className":1909,"style":718},[623],[574,1911,1913,1916],{"className":1912},[628],[574,1914,598],{"className":1915},[628,629],[574,1917,1919],{"className":1918},[728],[574,1920,1922,1942],{"className":1921},[732,733],[574,1923,1925,1939],{"className":1924},[737],[574,1926,1928],{"className":1927,"style":1556},[741],[574,1929,1930,1933],{"style":745},[574,1931],{"className":1932,"style":750},[749],[574,1934,1936],{"className":1935},[754,755,756,757],[574,1937,1488],{"className":1938},[628,757],[574,1940,765],{"className":1941},[764],[574,1943,1945],{"className":1944},[737],[574,1946,1948],{"className":1947,"style":772},[741],[574,1949],{},[574,1951],{"className":1952,"style":637},[636],[574,1954,602],{"className":1955},[641],[574,1957],{"className":1958,"style":637},[636],[574,1960,1962,1965],{"className":1961},[619],[574,1963],{"className":1964,"style":1342},[623],[574,1966,1488],{"className":1967},[628],". Die Matrix ist strikt diagonaldominant (",[574,1970,1972,1991],{"className":1971},[577],[574,1973,1975],{"className":1974},[581],[583,1976,1977],{"xmlns":585},[587,1978,1979,1988],{},[590,1980,1981,1983,1986],{},[918,1982,1473],{},[600,1984,1985],{},">",[918,1987,920],{},[607,1989,1990],{"encoding":609},"4 > 1",[574,1992,1994,2013],{"className":1993,"ariaHidden":615},[614],[574,1995,1997,2001,2004,2007,2010],{"className":1996},[619],[574,1998],{"className":1999,"style":2000},[623],"height:0.6835em;vertical-align:-0.0391em;",[574,2002,1473],{"className":2003},[628],[574,2005],{"className":2006,"style":637},[636],[574,2008,1985],{"className":2009},[641],[574,2011],{"className":2012,"style":637},[636],[574,2014,2016,2019],{"className":2015},[619],[574,2017],{"className":2018,"style":1342},[623],[574,2020,920],{"className":2021},[628],[574,2023,2025,2043],{"className":2024},[577],[574,2026,2028],{"className":2027},[581],[583,2029,2030],{"xmlns":585},[587,2031,2032,2040],{},[590,2033,2034,2036,2038],{},[918,2035,1510],{},[600,2037,1985],{},[918,2039,920],{},[607,2041,2042],{"encoding":609},"3 > 1",[574,2044,2046,2064],{"className":2045,"ariaHidden":615},[614],[574,2047,2049,2052,2055,2058,2061],{"className":2048},[619],[574,2050],{"className":2051,"style":2000},[623],[574,2053,1510],{"className":2054},[628],[574,2056],{"className":2057,"style":637},[636],[574,2059,1985],{"className":2060},[641],[574,2062],{"className":2063,"style":637},[636],[574,2065,2067,2070],{"className":2066},[619],[574,2068],{"className":2069,"style":1342},[623],[574,2071,920],{"className":2072},[628],"). Die Iterationsvorschrift lautet",[574,2075,2077],{"className":2076},[887],[574,2078,2080,2186],{"className":2079},[577],[574,2081,2083],{"className":2082},[581],[583,2084,2085],{"xmlns":585,"display":896},[587,2086,2087,2183],{},[590,2088,2089,2108,2110,2135,2137,2139,2157,2159],{},[2090,2091,2092,2094,2096],"msubsup",{},[593,2093,598],{},[918,2095,920],{},[590,2097,2098,2100,2102,2104,2106],{},[600,2099,911],{"stretchy":910},[593,2101,914],{},[600,2103,800],{},[918,2105,920],{},[600,2107,923],{"stretchy":910},[600,2109,602],{},[2111,2112,2113,2133],"mfrac",{},[590,2114,2115,2117,2119],{},[918,2116,1493],{},[600,2118,934],{},[2090,2120,2121,2123,2125],{},[593,2122,598],{},[918,2124,1488],{},[590,2126,2127,2129,2131],{},[600,2128,911],{"stretchy":910},[593,2130,914],{},[600,2132,923],{"stretchy":910},[918,2134,1473],{},[600,2136,1496],{"separator":615},[636,2138],{"width":1499},[2090,2140,2141,2143,2145],{},[593,2142,598],{},[918,2144,1488],{},[590,2146,2147,2149,2151,2153,2155],{},[600,2148,911],{"stretchy":910},[593,2150,914],{},[600,2152,800],{},[918,2154,920],{},[600,2156,923],{"stretchy":910},[600,2158,602],{},[2111,2160,2161,2181],{},[590,2162,2163,2165,2167],{},[918,2164,1521],{},[600,2166,934],{},[2090,2168,2169,2171,2173],{},[593,2170,598],{},[918,2172,920],{},[590,2174,2175,2177,2179],{},[600,2176,911],{"stretchy":910},[593,2178,914],{},[600,2180,923],{"stretchy":910},[918,2182,1510],{},[607,2184,2185],{"encoding":609},"x_1^{(k+1)} = \\frac{6 - x_2^{(k)}}{4}, \\qquad x_2^{(k+1)} = \\frac{7 - x_1^{(k)}}{3}",[574,2187,2189,2275,2506],{"className":2188,"ariaHidden":615},[614],[574,2190,2192,2196,2266,2269,2272],{"className":2191},[619],[574,2193],{"className":2194,"style":2195},[623],"height:1.3111em;vertical-align:-0.2663em;",[574,2197,2199,2202],{"className":2198},[628],[574,2200,598],{"className":2201},[628,629],[574,2203,2205],{"className":2204},[728],[574,2206,2208,2257],{"className":2207},[732,733],[574,2209,2211,2254],{"className":2210},[737],[574,2212,2215,2227],{"className":2213,"style":2214},[741],"height:1.0448em;",[574,2216,2218,2221],{"style":2217},"top:-2.4337em;margin-left:0em;margin-right:0.05em;",[574,2219],{"className":2220,"style":750},[749],[574,2222,2224],{"className":2223},[754,755,756,757],[574,2225,920],{"className":2226},[628,757],[574,2228,2230,2233],{"style":2229},"top:-3.2198em;margin-right:0.05em;",[574,2231],{"className":2232,"style":750},[749],[574,2234,2236],{"className":2235},[754,755,756,757],[574,2237,2239,2242,2245,2248,2251],{"className":2238},[628,757],[574,2240,911],{"className":2241},[1018,757],[574,2243,914],{"className":2244,"style":1022},[628,629,757],[574,2246,800],{"className":2247},[851,757],[574,2249,920],{"className":2250},[628,757],[574,2252,923],{"className":2253},[1032,757],[574,2255,765],{"className":2256},[764],[574,2258,2260],{"className":2259},[737],[574,2261,2264],{"className":2262,"style":2263},[741],"height:0.2663em;",[574,2265],{},[574,2267],{"className":2268,"style":637},[636],[574,2270,602],{"className":2271},[641],[574,2273],{"className":2274,"style":637},[636],[574,2276,2278,2282,2422,2425,2428,2431,2497,2500,2503],{"className":2277},[619],[574,2279],{"className":2280,"style":2281},[623],"height:2.4078em;vertical-align:-0.686em;",[574,2283,2285,2289,2419],{"className":2284},[628],[574,2286],{"className":2287},[1018,2288],"nulldelimiter",[574,2290,2292],{"className":2291},[2111],[574,2293,2295,2410],{"className":2294},[732,733],[574,2296,2298,2407],{"className":2297},[737],[574,2299,2302,2315,2326],{"className":2300,"style":2301},[741],"height:1.7218em;",[574,2303,2305,2309],{"style":2304},"top:-2.3588em;",[574,2306],{"className":2307,"style":2308},[749],"height:3.0448em;",[574,2310,2312],{"className":2311},[628],[574,2313,1473],{"className":2314},[628],[574,2316,2318,2321],{"style":2317},"top:-3.2748em;",[574,2319],{"className":2320,"style":2308},[749],[574,2322],{"className":2323,"style":2325},[2324],"frac-line","border-bottom-width:0.04em;",[574,2327,2329,2332],{"style":2328},"top:-3.7218em;",[574,2330],{"className":2331,"style":2308},[749],[574,2333,2335,2338,2341,2344,2347],{"className":2334},[628],[574,2336,1493],{"className":2337},[628],[574,2339],{"className":2340,"style":847},[636],[574,2342,934],{"className":2343},[851],[574,2345],{"className":2346,"style":847},[636],[574,2348,2350,2353],{"className":2349},[628],[574,2351,598],{"className":2352},[628,629],[574,2354,2356],{"className":2355},[728],[574,2357,2359,2399],{"className":2358},[732,733],[574,2360,2362,2396],{"className":2361},[737],[574,2363,2365,2376],{"className":2364,"style":2214},[741],[574,2366,2367,2370],{"style":2217},[574,2368],{"className":2369,"style":750},[749],[574,2371,2373],{"className":2372},[754,755,756,757],[574,2374,1488],{"className":2375},[628,757],[574,2377,2378,2381],{"style":2229},[574,2379],{"className":2380,"style":750},[749],[574,2382,2384],{"className":2383},[754,755,756,757],[574,2385,2387,2390,2393],{"className":2386},[628,757],[574,2388,911],{"className":2389},[1018,757],[574,2391,914],{"className":2392,"style":1022},[628,629,757],[574,2394,923],{"className":2395},[1032,757],[574,2397,765],{"className":2398},[764],[574,2400,2402],{"className":2401},[737],[574,2403,2405],{"className":2404,"style":2263},[741],[574,2406],{},[574,2408,765],{"className":2409},[764],[574,2411,2413],{"className":2412},[737],[574,2414,2417],{"className":2415,"style":2416},[741],"height:0.686em;",[574,2418],{},[574,2420],{"className":2421},[1032,2288],[574,2423,1496],{"className":2424},[1656],[574,2426],{"className":2427,"style":1660},[636],[574,2429],{"className":2430,"style":1143},[636],[574,2432,2434,2437],{"className":2433},[628],[574,2435,598],{"className":2436},[628,629],[574,2438,2440],{"className":2439},[728],[574,2441,2443,2489],{"className":2442},[732,733],[574,2444,2446,2486],{"className":2445},[737],[574,2447,2449,2460],{"className":2448,"style":2214},[741],[574,2450,2451,2454],{"style":2217},[574,2452],{"className":2453,"style":750},[749],[574,2455,2457],{"className":2456},[754,755,756,757],[574,2458,1488],{"className":2459},[628,757],[574,2461,2462,2465],{"style":2229},[574,2463],{"className":2464,"style":750},[749],[574,2466,2468],{"className":2467},[754,755,756,757],[574,2469,2471,2474,2477,2480,2483],{"className":2470},[628,757],[574,2472,911],{"className":2473},[1018,757],[574,2475,914],{"className":2476,"style":1022},[628,629,757],[574,2478,800],{"className":2479},[851,757],[574,2481,920],{"className":2482},[628,757],[574,2484,923],{"className":2485},[1032,757],[574,2487,765],{"className":2488},[764],[574,2490,2492],{"className":2491},[737],[574,2493,2495],{"className":2494,"style":2263},[741],[574,2496],{},[574,2498],{"className":2499,"style":637},[636],[574,2501,602],{"className":2502},[641],[574,2504],{"className":2505,"style":637},[636],[574,2507,2509,2512],{"className":2508},[619],[574,2510],{"className":2511,"style":2281},[623],[574,2513,2515,2518,2640],{"className":2514},[628],[574,2516],{"className":2517},[1018,2288],[574,2519,2521],{"className":2520},[2111],[574,2522,2524,2632],{"className":2523},[732,733],[574,2525,2527,2629],{"className":2526},[737],[574,2528,2530,2541,2549],{"className":2529,"style":2301},[741],[574,2531,2532,2535],{"style":2304},[574,2533],{"className":2534,"style":2308},[749],[574,2536,2538],{"className":2537},[628],[574,2539,1510],{"className":2540},[628],[574,2542,2543,2546],{"style":2317},[574,2544],{"className":2545,"style":2308},[749],[574,2547],{"className":2548,"style":2325},[2324],[574,2550,2551,2554],{"style":2328},[574,2552],{"className":2553,"style":2308},[749],[574,2555,2557,2560,2563,2566,2569],{"className":2556},[628],[574,2558,1521],{"className":2559},[628],[574,2561],{"className":2562,"style":847},[636],[574,2564,934],{"className":2565},[851],[574,2567],{"className":2568,"style":847},[636],[574,2570,2572,2575],{"className":2571},[628],[574,2573,598],{"className":2574},[628,629],[574,2576,2578],{"className":2577},[728],[574,2579,2581,2621],{"className":2580},[732,733],[574,2582,2584,2618],{"className":2583},[737],[574,2585,2587,2598],{"className":2586,"style":2214},[741],[574,2588,2589,2592],{"style":2217},[574,2590],{"className":2591,"style":750},[749],[574,2593,2595],{"className":2594},[754,755,756,757],[574,2596,920],{"className":2597},[628,757],[574,2599,2600,2603],{"style":2229},[574,2601],{"className":2602,"style":750},[749],[574,2604,2606],{"className":2605},[754,755,756,757],[574,2607,2609,2612,2615],{"className":2608},[628,757],[574,2610,911],{"className":2611},[1018,757],[574,2613,914],{"className":2614,"style":1022},[628,629,757],[574,2616,923],{"className":2617},[1032,757],[574,2619,765],{"className":2620},[764],[574,2622,2624],{"className":2623},[737],[574,2625,2627],{"className":2626,"style":2263},[741],[574,2628],{},[574,2630,765],{"className":2631},[764],[574,2633,2635],{"className":2634},[737],[574,2636,2638],{"className":2637,"style":2416},[741],[574,2639],{},[574,2641],{"className":2642},[1032,2288],[563,2644,2645,2646,2767],{},"Ab ",[574,2647,2649,2686],{"className":2648},[577],[574,2650,2652],{"className":2651},[581],[583,2653,2654],{"xmlns":585},[587,2655,2656,2683],{},[590,2657,2658,2671,2673,2675,2677,2679,2681],{},[902,2659,2660,2662],{},[593,2661,598],{},[590,2663,2664,2666,2669],{},[600,2665,911],{"stretchy":910},[918,2667,2668],{},"0",[600,2670,923],{"stretchy":910},[600,2672,602],{},[600,2674,911],{"stretchy":910},[918,2676,2668],{},[600,2678,1496],{"separator":615},[918,2680,2668],{},[600,2682,923],{"stretchy":910},[607,2684,2685],{"encoding":609},"x^{(0)} = (0, 0)",[574,2687,2689,2743],{"className":2688,"ariaHidden":615},[614],[574,2690,2692,2696,2734,2737,2740],{"className":2691},[619],[574,2693],{"className":2694,"style":2695},[623],"height:0.888em;",[574,2697,2699,2702],{"className":2698},[628],[574,2700,598],{"className":2701},[628,629],[574,2703,2705],{"className":2704},[728],[574,2706,2708],{"className":2707},[732],[574,2709,2711],{"className":2710},[737],[574,2712,2714],{"className":2713,"style":2695},[741],[574,2715,2716,2719],{"style":1273},[574,2717],{"className":2718,"style":750},[749],[574,2720,2722],{"className":2721},[754,755,756,757],[574,2723,2725,2728,2731],{"className":2724},[628,757],[574,2726,911],{"className":2727},[1018,757],[574,2729,2668],{"className":2730},[628,757],[574,2732,923],{"className":2733},[1032,757],[574,2735],{"className":2736,"style":637},[636],[574,2738,602],{"className":2739},[641],[574,2741],{"className":2742,"style":637},[636],[574,2744,2746,2749,2752,2755,2758,2761,2764],{"className":2745},[619],[574,2747],{"className":2748,"style":1111},[623],[574,2750,911],{"className":2751},[1018],[574,2753,2668],{"className":2754},[628],[574,2756,1496],{"className":2757},[1656],[574,2759],{"className":2760,"style":1143},[636],[574,2762,2668],{"className":2763},[628],[574,2765,923],{"className":2766},[1032],":",[2769,2770,2771,3008],"table",{},[2772,2773,2774],"thead",{},[2775,2776,2777,2808,2908],"tr",{},[2778,2779,2780],"th",{},[574,2781,2783,2796],{"className":2782},[577],[574,2784,2786],{"className":2785},[581],[583,2787,2788],{"xmlns":585},[587,2789,2790,2794],{},[590,2791,2792],{},[593,2793,914],{},[607,2795,914],{"encoding":609},[574,2797,2799],{"className":2798,"ariaHidden":615},[614],[574,2800,2802,2805],{"className":2801},[619],[574,2803],{"className":2804,"style":651},[623],[574,2806,914],{"className":2807,"style":1022},[628,629],[2778,2809,2810],{},[574,2811,2813,2839],{"className":2812},[577],[574,2814,2816],{"className":2815},[581],[583,2817,2818],{"xmlns":585},[587,2819,2820,2836],{},[590,2821,2822],{},[2090,2823,2824,2826,2828],{},[593,2825,598],{},[918,2827,920],{},[590,2829,2830,2832,2834],{},[600,2831,911],{"stretchy":910},[593,2833,914],{},[600,2835,923],{"stretchy":910},[607,2837,2838],{"encoding":609},"x_1^{(k)}",[574,2840,2842],{"className":2841,"ariaHidden":615},[614],[574,2843,2845,2848],{"className":2844},[619],[574,2846],{"className":2847,"style":2195},[623],[574,2849,2851,2854],{"className":2850},[628],[574,2852,598],{"className":2853},[628,629],[574,2855,2857],{"className":2856},[728],[574,2858,2860,2900],{"className":2859},[732,733],[574,2861,2863,2897],{"className":2862},[737],[574,2864,2866,2877],{"className":2865,"style":2214},[741],[574,2867,2868,2871],{"style":2217},[574,2869],{"className":2870,"style":750},[749],[574,2872,2874],{"className":2873},[754,755,756,757],[574,2875,920],{"className":2876},[628,757],[574,2878,2879,2882],{"style":2229},[574,2880],{"className":2881,"style":750},[749],[574,2883,2885],{"className":2884},[754,755,756,757],[574,2886,2888,2891,2894],{"className":2887},[628,757],[574,2889,911],{"className":2890},[1018,757],[574,2892,914],{"className":2893,"style":1022},[628,629,757],[574,2895,923],{"className":2896},[1032,757],[574,2898,765],{"className":2899},[764],[574,2901,2903],{"className":2902},[737],[574,2904,2906],{"className":2905,"style":2263},[741],[574,2907],{},[2778,2909,2910],{},[574,2911,2913,2939],{"className":2912},[577],[574,2914,2916],{"className":2915},[581],[583,2917,2918],{"xmlns":585},[587,2919,2920,2936],{},[590,2921,2922],{},[2090,2923,2924,2926,2928],{},[593,2925,598],{},[918,2927,1488],{},[590,2929,2930,2932,2934],{},[600,2931,911],{"stretchy":910},[593,2933,914],{},[600,2935,923],{"stretchy":910},[607,2937,2938],{"encoding":609},"x_2^{(k)}",[574,2940,2942],{"className":2941,"ariaHidden":615},[614],[574,2943,2945,2948],{"className":2944},[619],[574,2946],{"className":2947,"style":2195},[623],[574,2949,2951,2954],{"className":2950},[628],[574,2952,598],{"className":2953},[628,629],[574,2955,2957],{"className":2956},[728],[574,2958,2960,3000],{"className":2959},[732,733],[574,2961,2963,2997],{"className":2962},[737],[574,2964,2966,2977],{"className":2965,"style":2214},[741],[574,2967,2968,2971],{"style":2217},[574,2969],{"className":2970,"style":750},[749],[574,2972,2974],{"className":2973},[754,755,756,757],[574,2975,1488],{"className":2976},[628,757],[574,2978,2979,2982],{"style":2229},[574,2980],{"className":2981,"style":750},[749],[574,2983,2985],{"className":2984},[754,755,756,757],[574,2986,2988,2991,2994],{"className":2987},[628,757],[574,2989,911],{"className":2990},[1018,757],[574,2992,914],{"className":2993,"style":1022},[628,629,757],[574,2995,923],{"className":2996},[1032,757],[574,2998,765],{"className":2999},[764],[574,3001,3003],{"className":3002},[737],[574,3004,3006],{"className":3005,"style":2263},[741],[574,3007],{},[3009,3010,3011,3022,3032],"tbody",{},[2775,3012,3013,3016,3019],{},[3014,3015,920],"td",{},[3014,3017,3018],{},"1,5",[3014,3020,3021],{},"2,3333",[2775,3023,3024,3026,3029],{},[3014,3025,1488],{},[3014,3027,3028],{},"0,9167",[3014,3030,3031],{},"1,8333",[2775,3033,3034,3036,3039],{},[3014,3035,1510],{},[3014,3037,3038],{},"1,0417",[3014,3040,3041],{},"2,0278",[563,3043,3044,3045,3194,3195,3235],{},"Die Iterationsmatrix hat die Eigenwerte ",[574,3046,3048,3084],{"className":3047},[577],[574,3049,3051],{"className":3050},[581],[583,3052,3053],{"xmlns":585},[587,3054,3055,3081],{},[590,3056,3057,3060,3073,3076,3078],{},[600,3058,3059],{},"±",[3061,3062,3063],"msqrt",{},[590,3064,3065,3067,3070],{},[918,3066,920],{},[593,3068,3069],{"mathvariant":1368},"\u002F",[918,3071,3072],{},"12",[600,3074,3075],{},"≈",[600,3077,3059],{},[918,3079,3080],{},"0,2887",[607,3082,3083],{"encoding":609},"\\pm\\sqrt{1\u002F12} \\approx \\pm 0{,}2887",[574,3085,3087,3172],{"className":3086,"ariaHidden":615},[614],[574,3088,3090,3094,3097,3163,3166,3169],{"className":3089},[619],[574,3091],{"className":3092,"style":3093},[623],"height:1.24em;vertical-align:-0.305em;",[574,3095,3059],{"className":3096},[628],[574,3098,3101],{"className":3099},[628,3100],"sqrt",[574,3102,3104,3154],{"className":3103},[732,733],[574,3105,3107,3151],{"className":3106},[737],[574,3108,3111,3128],{"className":3109,"style":3110},[741],"height:0.935em;",[574,3112,3116,3120],{"className":3113,"style":3115},[3114],"svg-align","top:-3.2em;",[574,3117],{"className":3118,"style":3119},[749],"height:3.2em;",[574,3121,3124],{"className":3122,"style":3123},[628],"padding-left:1em;",[574,3125,3127],{"className":3126},[628],"1\u002F12",[574,3129,3131,3134],{"style":3130},"top:-2.895em;",[574,3132],{"className":3133,"style":3119},[749],[574,3135,3139],{"className":3136,"style":3138},[3137],"hide-tail","min-width:1.02em;height:1.28em;",[3140,3141,3147],"svg",{"xmlns":3142,"width":3143,"height":3144,"viewBox":3145,"preserveAspectRatio":3146},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.28em","0 0 400000 1296","xMinYMin slice",[3148,3149],"path",{"d":3150},"M263,681c0.7,0,18,39.7,52,119\nc34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120\nc340,-704.7,510.7,-1060.3,512,-1067\nl0 -0\nc4.7,-7.3,11,-11,19,-11\nH40000v40H1012.3\ns-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232\nc-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1\ns-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26\nc-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z\nM1001 80h400000v40h-400000z",[574,3152,765],{"className":3153},[764],[574,3155,3157],{"className":3156},[737],[574,3158,3161],{"className":3159,"style":3160},[741],"height:0.305em;",[574,3162],{},[574,3164],{"className":3165,"style":637},[636],[574,3167,3075],{"className":3168},[641],[574,3170],{"className":3171,"style":637},[636],[574,3173,3175,3178,3181,3184,3190],{"className":3174},[619],[574,3176],{"className":3177,"style":1649},[623],[574,3179,3059],{"className":3180},[628],[574,3182,2668],{"className":3183},[628],[574,3185,3187],{"className":3186},[628],[574,3188,1496],{"className":3189},[1656],[574,3191,3193],{"className":3192},[628],"2887",". Der Fehler schrumpft also pro Schritt etwa auf das ",[574,3196,3198,3213],{"className":3197},[577],[574,3199,3201],{"className":3200},[581],[583,3202,3203],{"xmlns":585},[587,3204,3205,3210],{},[590,3206,3207],{},[918,3208,3209],{},"0,29",[607,3211,3212],{"encoding":609},"0{,}29",[574,3214,3216],{"className":3215,"ariaHidden":615},[614],[574,3217,3219,3222,3225,3231],{"className":3218},[619],[574,3220],{"className":3221,"style":1649},[623],[574,3223,2668],{"className":3224},[628],[574,3226,3228],{"className":3227},[628],[574,3229,1496],{"className":3230},[1656],[574,3232,3234],{"className":3233},[628],"29","-Fache.",[558,3237,3239],{"id":3238},"typische-fehler","Typische Fehler",[1192,3241,3242,3245,3248,3251],{},[1195,3243,3244],{},"Neu berechnete Komponenten schon im selben Schritt verwenden. Das ist das Gauß-Seidel-Verfahren, nicht Jacobi.",[1195,3246,3247],{},"Das Verfahren bei einer Null auf der Diagonalen anwenden. Vorher Zeilen tauschen.",[1195,3249,3250],{},"Aus fehlender Diagonaldominanz schließen, dass das Verfahren divergiert. Diagonaldominanz ist hinreichend, aber nicht notwendig.",[1195,3252,3253,3254,3367],{},"Nach einer festen Zahl von Schritten abbrechen, ohne das Residuum ",[574,3255,3257,3292],{"className":3256},[577],[574,3258,3260],{"className":3259},[581],[583,3261,3262],{"xmlns":585},[587,3263,3264,3289],{},[590,3265,3266,3269,3271,3273,3275,3287],{},[593,3267,3268],{"mathvariant":1368},"∥",[593,3270,605],{},[600,3272,934],{},[593,3274,595],{},[902,3276,3277,3279],{},[593,3278,598],{},[590,3280,3281,3283,3285],{},[600,3282,911],{"stretchy":910},[593,3284,914],{},[600,3286,923],{"stretchy":910},[593,3288,3268],{"mathvariant":1368},[607,3290,3291],{"encoding":609},"\\|b - Ax^{(k)}\\|",[574,3293,3295,3316],{"className":3294,"ariaHidden":615},[614],[574,3296,3298,3301,3304,3307,3310,3313],{"className":3297},[619],[574,3299],{"className":3300,"style":1111},[623],[574,3302,3268],{"className":3303},[628],[574,3305,605],{"className":3306},[628,629],[574,3308],{"className":3309,"style":847},[636],[574,3311,934],{"className":3312},[851],[574,3314],{"className":3315,"style":847},[636],[574,3317,3319,3323,3326,3364],{"className":3318},[619],[574,3320],{"className":3321,"style":3322},[623],"height:1.138em;vertical-align:-0.25em;",[574,3324,595],{"className":3325},[628,629],[574,3327,3329,3332],{"className":3328},[628],[574,3330,598],{"className":3331},[628,629],[574,3333,3335],{"className":3334},[728],[574,3336,3338],{"className":3337},[732],[574,3339,3341],{"className":3340},[737],[574,3342,3344],{"className":3343,"style":2695},[741],[574,3345,3346,3349],{"style":1273},[574,3347],{"className":3348,"style":750},[749],[574,3350,3352],{"className":3351},[754,755,756,757],[574,3353,3355,3358,3361],{"className":3354},[628,757],[574,3356,911],{"className":3357},[1018,757],[574,3359,914],{"className":3360,"style":1022},[628,629,757],[574,3362,923],{"className":3363},[1032,757],[574,3365,3268],{"className":3366},[628]," oder die Änderung zwischen zwei Schritten zu prüfen.",{"title":3369,"searchDepth":3370,"depth":3370,"links":3371},"",2,[3372,3373,3374],{"id":560,"depth":3370,"text":561},{"id":1451,"depth":3370,"text":1452},{"id":3238,"depth":3370,"text":3239},[3376,3378,3380,3383,3386,3389,3392,3395,3398,3401,3404,3407,3410],{"lhs":3377,"rhs":920},"(6 - 1*2)\u002F4",{"lhs":3379,"rhs":1488},"(7 - 1*1)\u002F3",{"lhs":3381,"rhs":3382},"(6 - 0)\u002F4","1.5",{"lhs":3384,"rhs":3385},"round((7 - 0)\u002F3, 4)","2.3333",{"lhs":3387,"rhs":3388},"(6 - 7\u002F3)\u002F4","11\u002F12",{"lhs":3390,"rhs":3391},"round(11\u002F12, 4)","0.9167",{"lhs":3393,"rhs":3394},"round((7 - 1.5)\u002F3, 4)","1.8333",{"lhs":3396,"rhs":3397},"(6 - 5.5\u002F3)\u002F4","25\u002F24",{"lhs":3399,"rhs":3400},"round(25\u002F24, 4)","1.0417",{"lhs":3402,"rhs":3403},"(7 - 11\u002F12)\u002F3","73\u002F36",{"lhs":3405,"rhs":3406},"round(73\u002F36, 4)","2.0278",{"lhs":3408,"rhs":3409},"round(sqrt(1\u002F4*1\u002F3), 4)","0.2887",{"lhs":3411,"rhs":3412},"det([[0 - u, -1\u002F4], [-1\u002F3, 0 - u]])","u^2 - 1\u002F12","A x = b,\\ a_{ii} \\neq 0,\\ i = 1, \\ldots, n","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A x = b,\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\">A\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\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:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\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>a\u003C\u002Fmi>\u003Cmrow>\u003Cmi>i\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmsub>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a_{ii} \\neq 0,\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:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;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=\"mord mathnormal mtight\">ii\u003C\u002Fspan>\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=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">\u003Cspan class=\"mrel\">\u003Cspan class=\"mord katex-vbox\">\u003Cspan class=\"katex-thinbox\">\u003Cspan class=\"rlap\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-inner\">\u003Cspan class=\"mord\">\u003Cspan class=\"mrel\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-fix\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace nobreak\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\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>\u003Cmi>i\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmo>…\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">i = 1, \\ldots, 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:0.6595em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">i\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:0.8389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">…\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","jacobi-method","x_i^{(k+1)} = \\frac{1}{a_{ii}} \\Bigl( b_i - \\sum_{j \\neq i} a_{ij}\\,x_j^{(k)} \\Bigr)","\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>\u003Cmsubsup>\u003Cmi>x\u003C\u002Fmi>\u003Cmi>i\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\u002Fmsubsup>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmn>1\u003C\u002Fmn>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmrow>\u003Cmi>i\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmsub>\u003C\u002Fmfrac>\u003Cmo fence=\"true\" stretchy=\"true\" minsize=\"1.8em\" maxsize=\"1.8em\">(\u003C\u002Fmo>\u003Cmsub>\u003Cmi>b\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>−\u003C\u002Fmo>\u003Cmunder>\u003Cmo>∑\u003C\u002Fmo>\u003Cmrow>\u003Cmi>j\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmunder>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmrow>\u003Cmi>i\u003C\u002Fmi>\u003Cmi>j\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmsub>\u003Cmtext> \u003C\u002Fmtext>\u003Cmsubsup>\u003Cmi>x\u003C\u002Fmi>\u003Cmi>j\u003C\u002Fmi>\u003Cmrow>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>k\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmsubsup>\u003Cmo fence=\"true\" stretchy=\"true\" minsize=\"1.8em\" maxsize=\"1.8em\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x_i^{(k+1)} = \\frac{1}{a_{ii}} \\Bigl( b_i - \\sum_{j \\neq i} a_{ij}\\,x_j^{(k)} \\Bigr)\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:1.3217em;vertical-align:-0.2769em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.0448em;\">\u003Cspan style=\"top:-2.4231em;margin-left:0em;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\">i\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.2198em;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>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.2769em;\">\u003Cspan>\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:2.1574em;vertical-align:-0.836em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3214em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;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=\"mord mathnormal mtight\">ii\u003C\u002Fspan>\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>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">1\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:0.836em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">\u003Cspan class=\"delimsizing size2\">(\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;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\">i\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=\"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:2.5882em;vertical-align:-1.4382em;\">\u003C\u002Fspan>\u003Cspan class=\"mop op-limits\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.05em;\">\u003Cspan style=\"top:-1.8479em;margin-left:0em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0572em;\">j\u003C\u002Fspan>\u003Cspan class=\"mrel mtight\">\u003Cspan class=\"mrel mtight\">\u003Cspan class=\"mord katex-vbox mtight\">\u003Cspan class=\"katex-thinbox mtight\">\u003Cspan class=\"rlap mtight\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-inner\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mrel mtight\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-fix\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace nobreak mtight\">\u003C\u002Fspan>\u003Cspan class=\"mrel mtight\">=\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\">i\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.05em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan>\u003Cspan class=\"mop op-symbol large-op\">∑\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:1.4382em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;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=\"mord mathnormal mtight\" style=\"margin-right:0.0572em;\">ij\u003C\u002Fspan>\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:0.2861em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\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 vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.0448em;\">\u003Cspan style=\"top:-2.4231em;margin-left:0em;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:0.0572em;\">j\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.2198em;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>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.413em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">\u003Cspan class=\"delimsizing size2\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fnumerics\u002Fjacobi-verfahren",[],[3426,3427,3428,3429],"gauss-seidel-method","fixed-point-iteration","gaussian-elimination","condition-number",{"title":548,"description":3369},"de\u002Fformulas\u002Fmath\u002Fnumerics\u002Fjacobi-verfahren","Das Jacobi-Verfahren löst jede Gleichung nach ihrer Diagonalvariablen auf und setzt die alte Näherung für alle anderen ein.",[3434,3435,3436,3437],"lineares gleichungssystem","iterationsverfahren","diagonaldominanz","gesamtschrittverfahren",[3439,3443,3447,3451,3455],{"symbol":3440,"meaning":3441,"symbolHtml":3442},"x_i^{(k)}","i-te Komponente der Näherung nach k Schritten","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsubsup>\u003Cmi>x\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003Cmrow>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>k\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmsubsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x_i^{(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:1.3217em;vertical-align:-0.2769em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.0448em;\">\u003Cspan style=\"top:-2.4231em;margin-left:0em;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\">i\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.2198em;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>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.2769em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":3444,"meaning":3445,"symbolHtml":3446},"a_{ij}","Einträge der Koeffizientenmatrix A","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmrow>\u003Cmi>i\u003C\u002Fmi>\u003Cmi>j\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a_{ij}\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:0.7167em;vertical-align:-0.2861em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;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=\"mord mathnormal mtight\" style=\"margin-right:0.0572em;\">ij\u003C\u002Fspan>\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:0.2861em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":3448,"meaning":3449,"symbolHtml":3450},"a_{ii}","Diagonaleinträge von A","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmrow>\u003Cmi>i\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a_{ii}\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:0.5806em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;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=\"mord mathnormal mtight\">ii\u003C\u002Fspan>\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":3452,"meaning":3453,"symbolHtml":3454},"b_i","Komponenten der rechten Seite b","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>b\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">b_i\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:0.8444em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;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\">i\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":3456,"meaning":3457,"symbolHtml":3458},"n","Anzahl der Gleichungen und Unbekannten","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">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:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","R1VR1bCMnXp9K3iiIy2h_np4uM6aOUw1_XbX9pMYT54",[3461,3464,3467,3470],{"stem":3462,"title":3463,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fgauss-algorithmus","Gauß-Algorithmus",{"stem":3465,"title":3466,"category":391},"de\u002Fformulas\u002Fmath\u002Fnumerics\u002Ffixpunktiteration","Fixpunktiteration",{"stem":3468,"title":3469,"category":391},"de\u002Fformulas\u002Fmath\u002Fnumerics\u002Fgauss-seidel-verfahren","Gauß-Seidel-Verfahren",{"stem":3471,"title":3472,"category":391},"de\u002Fformulas\u002Fmath\u002Fnumerics\u002Fkonditionszahl","Konditionszahl",1793824265727]