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gilt.",[1171,1172,1173,1424,1670],"ul",{},[1174,1175,1176,1179,1180,1232,1233,1286,1287,1316,1317,1423],"li",{},[568,1177,1178],{},"Linear"," (",[572,1181,1183,1201],{"className":1182},[575],[572,1184,1186],{"className":1185},[579],[581,1187,1188],{"xmlns":583},[585,1189,1190,1198],{},[588,1191,1192,1194,1196],{},[594,1193,564],{},[697,1195,766],{},[1005,1197,1007],{},[601,1199,1200],{"encoding":603},"p = 1",[572,1202,1204,1222],{"className":1203,"ariaHidden":609},[608],[572,1205,1207,1210,1213,1216,1219],{"className":1206},[613],[572,1208],{"className":1209,"style":976},[617],[572,1211,564],{"className":1212},[622,626],[572,1214],{"className":1215,"style":844},[843],[572,1217,766],{"className":1218},[848],[572,1220],{"className":1221,"style":844},[843],[572,1223,1225,1229],{"className":1224},[613],[572,1226],{"className":1227,"style":1228},[617],"height:0.6444em;",[572,1230,1007],{"className":1231},[622],", ",[572,1234,1236,1255],{"className":1235},[575],[572,1237,1239],{"className":1238},[579],[581,1240,1241],{"xmlns":583},[585,1242,1243,1252],{},[588,1244,1245,1247,1250],{},[594,1246,1013],{},[697,1248,1249],{},"\u003C",[1005,1251,1007],{},[601,1253,1254],{"encoding":603},"C \u003C 1",[572,1256,1258,1277],{"className":1257,"ariaHidden":609},[608],[572,1259,1261,1265,1268,1271,1274],{"className":1260},[613],[572,1262],{"className":1263,"style":1264},[617],"height:0.7224em;vertical-align:-0.0391em;",[572,1266,1013],{"className":1267,"style":1109},[622,626],[572,1269],{"className":1270,"style":844},[843],[572,1272,1249],{"className":1273},[848],[572,1275],{"className":1276,"style":844},[843],[572,1278,1280,1283],{"className":1279},[613],[572,1281],{"className":1282,"style":1228},[617],[572,1284,1007],{"className":1285},[622],"): Der Fehler wird pro Schritt um den Faktor ",[572,1288,1290,1303],{"className":1289},[575],[572,1291,1293],{"className":1292},[579],[581,1294,1295],{"xmlns":583},[585,1296,1297,1301],{},[588,1298,1299],{},[594,1300,1013],{},[601,1302,1013],{"encoding":603},[572,1304,1306],{"className":1305,"ariaHidden":609},[608],[572,1307,1309,1313],{"className":1308},[613],[572,1310],{"className":1311,"style":1312},[617],"height:0.6833em;",[572,1314,1013],{"className":1315,"style":1109},[622,626]," kleiner. Man gewinnt pro Schritt etwa ",[572,1318,1320,1349],{"className":1319},[575],[572,1321,1323],{"className":1322},[579],[581,1324,1325],{"xmlns":583},[585,1326,1327,1346],{},[588,1328,1329,1331,1344],{},[697,1330,779],{},[591,1332,1333,1341],{},[588,1334,1335,1338],{},[594,1336,1337],{},"log",[697,1339,1340],{},"⁡",[1005,1342,1343],{},"10",[594,1345,1013],{},[601,1347,1348],{"encoding":603},"-\\log_{10} C",[572,1350,1352],{"className":1351,"ariaHidden":609},[608],[572,1353,1355,1359,1362,1365,1417,1420],{"className":1354},[613],[572,1356],{"className":1357,"style":1358},[617],"height:0.9386em;vertical-align:-0.2441em;",[572,1360,779],{"className":1361},[622],[572,1363],{"className":1364,"style":1113},[843],[572,1366,1369,1377],{"className":1367},[1368],"mop",[572,1370,1372,1373],{"className":1371},[1368],"lo",[572,1374,1376],{"style":1375},"margin-right:0.0139em;","g",[572,1378,1380],{"className":1379},[630],[572,1381,1383,1408],{"className":1382},[634,635],[572,1384,1386,1405],{"className":1385},[639],[572,1387,1390],{"className":1388,"style":1389},[643],"height:0.207em;",[572,1391,1393,1396],{"style":1392},"top:-2.4559em;margin-right:0.05em;",[572,1394],{"className":1395,"style":652},[651],[572,1397,1399],{"className":1398},[656,657,658,659],[572,1400,1402],{"className":1401},[622,659],[572,1403,1343],{"className":1404},[622,659],[572,1406,668],{"className":1407},[667],[572,1409,1411],{"className":1410},[639],[572,1412,1415],{"className":1413,"style":1414},[643],"height:0.2441em;",[572,1416],{},[572,1418],{"className":1419,"style":1113},[843],[572,1421,1013],{"className":1422,"style":1109},[622,626]," Dezimalstellen.",[1174,1425,1426,1429,1430,1669],{},[568,1427,1428],{},"Superlinear",": ",[572,1431,1433,1472],{"className":1432},[575],[572,1434,1436],{"className":1435},[579],[581,1437,1438],{"xmlns":583},[585,1439,1440,1469],{},[588,1441,1442,1463,1466],{},[1443,1444,1445,1457],"mfrac",{},[591,1446,1447,1449],{},[594,1448,761],{},[588,1450,1451,1453,1455],{},[594,1452,599],{},[697,1454,1003],{},[1005,1456,1007],{},[591,1458,1459,1461],{},[594,1460,761],{},[594,1462,599],{},[697,1464,1465],{},"→",[1005,1467,1468],{},"0",[601,1470,1471],{"encoding":603},"\\frac{e_{k+1}}{e_k} \\to 0",[572,1473,1475,1660],{"className":1474,"ariaHidden":609},[608],[572,1476,1478,1482,1651,1654,1657],{"className":1477},[613],[572,1479],{"className":1480,"style":1481},[617],"height:1.2098em;vertical-align:-0.4509em;",[572,1483,1485,1490,1647],{"className":1484},[622],[572,1486],{"className":1487},[1488,1489],"mopen","nulldelimiter",[572,1491,1493],{"className":1492},[1443],[572,1494,1496,1638],{"className":1495},[634,635],[572,1497,1499,1635],{"className":1498},[639],[572,1500,1503,1562,1573],{"className":1501,"style":1502},[643],"height:0.7589em;",[572,1504,1506,1510],{"style":1505},"top:-2.655em;",[572,1507],{"className":1508,"style":1509},[651],"height:3em;",[572,1511,1513],{"className":1512},[656,657,658,659],[572,1514,1516],{"className":1515},[622,659],[572,1517,1519,1522],{"className":1518},[622,659],[572,1520,761],{"className":1521},[622,626,659],[572,1523,1525],{"className":1524},[630],[572,1526,1528,1553],{"className":1527},[634,635],[572,1529,1531,1550],{"className":1530},[639],[572,1532,1535],{"className":1533,"style":1534},[643],"height:0.3448em;",[572,1536,1538,1542],{"style":1537},"top:-2.3488em;margin-left:0em;margin-right:0.0714em;",[572,1539],{"className":1540,"style":1541},[651],"height:2.5em;",[572,1543,1547],{"className":1544},[656,1545,1546,659],"reset-size3","size1",[572,1548,599],{"className":1549,"style":663},[622,626,659],[572,1551,668],{"className":1552},[667],[572,1554,1556],{"className":1555},[639],[572,1557,1560],{"className":1558,"style":1559},[643],"height:0.1512em;",[572,1561],{},[572,1563,1565,1568],{"style":1564},"top:-3.23em;",[572,1566],{"className":1567,"style":1509},[651],[572,1569],{"className":1570,"style":1572},[1571],"frac-line","border-bottom-width:0.04em;",[572,1574,1576,1579],{"style":1575},"top:-3.4575em;",[572,1577],{"className":1578,"style":1509},[651],[572,1580,1582],{"className":1581},[656,657,658,659],[572,1583,1585],{"className":1584},[622,659],[572,1586,1588,1591],{"className":1587},[622,659],[572,1589,761],{"className":1590},[622,626,659],[572,1592,1594],{"className":1593},[630],[572,1595,1597,1626],{"className":1596},[634,635],[572,1598,1600,1623],{"className":1599},[639],[572,1601,1603],{"className":1602,"style":1534},[643],[572,1604,1605,1608],{"style":1537},[572,1606],{"className":1607,"style":1541},[651],[572,1609,1611],{"className":1610},[656,1545,1546,659],[572,1612,1614,1617,1620],{"className":1613},[622,659],[572,1615,599],{"className":1616,"style":663},[622,626,659],[572,1618,1003],{"className":1619},[743,659],[572,1621,1007],{"className":1622},[622,659],[572,1624,668],{"className":1625},[667],[572,1627,1629],{"className":1628},[639],[572,1630,1633],{"className":1631,"style":1632},[643],"height:0.2107em;",[572,1634],{},[572,1636,668],{"className":1637},[667],[572,1639,1641],{"className":1640},[639],[572,1642,1645],{"className":1643,"style":1644},[643],"height:0.4509em;",[572,1646],{},[572,1648],{"className":1649},[1650,1489],"mclose",[572,1652],{"className":1653,"style":844},[843],[572,1655,1465],{"className":1656},[848],[572,1658],{"className":1659,"style":844},[843],[572,1661,1663,1666],{"className":1662},[613],[572,1664],{"className":1665,"style":1228},[617],[572,1667,1468],{"className":1668},[622],", also schneller als jede lineare Rate.",[1174,1671,1672,1179,1675,1727],{},[568,1673,1674],{},"Quadratisch",[572,1676,1678,1697],{"className":1677},[575],[572,1679,1681],{"className":1680},[579],[581,1682,1683],{"xmlns":583},[585,1684,1685,1694],{},[588,1686,1687,1689,1691],{},[594,1688,564],{},[697,1690,766],{},[1005,1692,1693],{},"2",[601,1695,1696],{"encoding":603},"p = 2",[572,1698,1700,1718],{"className":1699,"ariaHidden":609},[608],[572,1701,1703,1706,1709,1712,1715],{"className":1702},[613],[572,1704],{"className":1705,"style":976},[617],[572,1707,564],{"className":1708},[622,626],[572,1710],{"className":1711,"style":844},[843],[572,1713,766],{"className":1714},[848],[572,1716],{"className":1717,"style":844},[843],[572,1719,1721,1724],{"className":1720},[613],[572,1722],{"className":1723,"style":1228},[617],[572,1725,1693],{"className":1726},[622],"): Die Zahl der richtigen Stellen verdoppelt sich ungefähr in jedem Schritt.",[564,1729,1730],{},"Typische Werte:",[1732,1733,1734,1747],"table",{},[1735,1736,1737],"thead",{},[1738,1739,1740,1744],"tr",{},[1741,1742,1743],"th",{},"Verfahren",[1741,1745,1746],{},"Ordnung",[1748,1749,1750,1884,2209,2452],"tbody",{},[1738,1751,1752,1756],{},[1753,1754,1755],"td",{},"Bisektion",[1753,1757,1758,1759,1883],{},"linear mit ",[572,1760,1762,1784],{"className":1761},[575],[572,1763,1765],{"className":1764},[579],[581,1766,1767],{"xmlns":583},[585,1768,1769,1781],{},[588,1770,1771,1773,1775],{},[594,1772,1013],{},[697,1774,766],{},[1443,1776,1777,1779],{},[1005,1778,1007],{},[1005,1780,1693],{},[601,1782,1783],{"encoding":603},"C = \\frac{1}{2}",[572,1785,1787,1805],{"className":1786,"ariaHidden":609},[608],[572,1788,1790,1793,1796,1799,1802],{"className":1789},[613],[572,1791],{"className":1792,"style":1312},[617],[572,1794,1013],{"className":1795,"style":1109},[622,626],[572,1797],{"className":1798,"style":844},[843],[572,1800,766],{"className":1801},[848],[572,1803],{"className":1804,"style":844},[843],[572,1806,1808,1812],{"className":1807},[613],[572,1809],{"className":1810,"style":1811},[617],"height:1.1901em;vertical-align:-0.345em;",[572,1813,1815,1818,1880],{"className":1814},[622],[572,1816],{"className":1817},[1488,1489],[572,1819,1821],{"className":1820},[1443],[572,1822,1824,1871],{"className":1823},[634,635],[572,1825,1827,1868],{"className":1826},[639],[572,1828,1831,1845,1853],{"className":1829,"style":1830},[643],"height:0.8451em;",[572,1832,1833,1836],{"style":1505},[572,1834],{"className":1835,"style":1509},[651],[572,1837,1839],{"className":1838},[656,657,658,659],[572,1840,1842],{"className":1841},[622,659],[572,1843,1693],{"className":1844},[622,659],[572,1846,1847,1850],{"style":1564},[572,1848],{"className":1849,"style":1509},[651],[572,1851],{"className":1852,"style":1572},[1571],[572,1854,1856,1859],{"style":1855},"top:-3.394em;",[572,1857],{"className":1858,"style":1509},[651],[572,1860,1862],{"className":1861},[656,657,658,659],[572,1863,1865],{"className":1864},[622,659],[572,1866,1007],{"className":1867},[622,659],[572,1869,668],{"className":1870},[667],[572,1872,1874],{"className":1873},[639],[572,1875,1878],{"className":1876,"style":1877},[643],"height:0.345em;",[572,1879],{},[572,1881],{"className":1882},[1650,1489]," (Fehlerschranke)",[1738,1885,1886,1889],{},[1753,1887,1888],{},"Fixpunktiteration",[1753,1890,1758,1891,2037,2038],{},[572,1892,1894,1936],{"className":1893},[575],[572,1895,1897],{"className":1896},[579],[581,1898,1899],{"xmlns":583},[585,1900,1901,1933],{},[588,1902,1903,1905,1908,1911,1919,1922,1928,1931],{},[594,1904,1013],{},[697,1906,1907],{},"≈",[697,1909,770],{"stretchy":1910},"false",[692,1912,1913,1915],{},[594,1914,1376],{},[697,1916,1918],{"mathvariant":769,"lspace":1917,"rspace":1917},"0em","′",[697,1920,1921],{"stretchy":1910},"(",[692,1923,1924,1926],{},[594,1925,596],{},[697,1927,699],{},[697,1929,1930],{"stretchy":1910},")",[697,1932,770],{"stretchy":1910},[601,1934,1935],{"encoding":603},"C \\approx \\lvert g'(x^*) \\rvert",[572,1937,1939,1957],{"className":1938,"ariaHidden":609},[608],[572,1940,1942,1945,1948,1951,1954],{"className":1941},[613],[572,1943],{"className":1944,"style":1312},[617],[572,1946,1013],{"className":1947,"style":1109},[622,626],[572,1949],{"className":1950,"style":844},[843],[572,1952,1907],{"className":1953},[848],[572,1955],{"className":1956,"style":844},[843],[572,1958,1960,1964,1967,2001,2004,2033],{"className":1959},[613],[572,1961],{"className":1962,"style":1963},[617],"height:1.0019em;vertical-align:-0.25em;",[572,1965,770],{"className":1966},[1488],[572,1968,1970,1974],{"className":1969},[622],[572,1971,1376],{"className":1972,"style":1973},[622,626],"margin-right:0.0359em;",[572,1975,1977],{"className":1976},[630],[572,1978,1980],{"className":1979},[634],[572,1981,1983],{"className":1982},[639],[572,1984,1987],{"className":1985,"style":1986},[643],"height:0.7519em;",[572,1988,1989,1992],{"style":733},[572,1990],{"className":1991,"style":652},[651],[572,1993,1995],{"className":1994},[656,657,658,659],[572,1996,1998],{"className":1997},[622,659],[572,1999,1918],{"className":2000},[622,659],[572,2002,1921],{"className":2003},[1488],[572,2005,2007,2010],{"className":2006},[622],[572,2008,596],{"className":2009},[622,626],[572,2011,2013],{"className":2012},[630],[572,2014,2016],{"className":2015},[634],[572,2017,2019],{"className":2018},[639],[572,2020,2022],{"className":2021,"style":712},[643],[572,2023,2024,2027],{"style":733},[572,2025],{"className":2026,"style":652},[651],[572,2028,2030],{"className":2029},[656,657,658,659],[572,2031,699],{"className":2032},[743,659],[572,2034,2036],{"className":2035},[1650],")∣",", falls ",[572,2039,2041,2074],{"className":2040},[575],[572,2042,2044],{"className":2043},[579],[581,2045,2046],{"xmlns":583},[585,2047,2048,2071],{},[588,2049,2050,2056,2058,2064,2066,2069],{},[692,2051,2052,2054],{},[594,2053,1376],{},[697,2055,1918],{"mathvariant":769,"lspace":1917,"rspace":1917},[697,2057,1921],{"stretchy":1910},[692,2059,2060,2062],{},[594,2061,596],{},[697,2063,699],{},[697,2065,1930],{"stretchy":1910},[697,2067,2068],{"mathvariant":769},"≠",[1005,2070,1468],{},[601,2072,2073],{"encoding":603},"g'(x^*) \\neq 0",[572,2075,2077,2200],{"className":2076,"ariaHidden":609},[608],[572,2078,2080,2083,2115,2118,2147,2150,2153,2197],{"className":2079},[613],[572,2081],{"className":2082,"style":1963},[617],[572,2084,2086,2089],{"className":2085},[622],[572,2087,1376],{"className":2088,"style":1973},[622,626],[572,2090,2092],{"className":2091},[630],[572,2093,2095],{"className":2094},[634],[572,2096,2098],{"className":2097},[639],[572,2099,2101],{"className":2100,"style":1986},[643],[572,2102,2103,2106],{"style":733},[572,2104],{"className":2105,"style":652},[651],[572,2107,2109],{"className":2108},[656,657,658,659],[572,2110,2112],{"className":2111},[622,659],[572,2113,1918],{"className":2114},[622,659],[572,2116,1921],{"className":2117},[1488],[572,2119,2121,2124],{"className":2120},[622],[572,2122,596],{"className":2123},[622,626],[572,2125,2127],{"className":2126},[630],[572,2128,2130],{"className":2129},[634],[572,2131,2133],{"className":2132},[639],[572,2134,2136],{"className":2135,"style":712},[643],[572,2137,2138,2141],{"style":733},[572,2139],{"className":2140,"style":652},[651],[572,2142,2144],{"className":2143},[656,657,658,659],[572,2145,699],{"className":2146},[743,659],[572,2148,1930],{"className":2149},[1650],[572,2151],{"className":2152,"style":844},[843],[572,2154,2156,2190,2194],{"className":2155},[848],[572,2157,2159],{"className":2158},[848],[572,2160,2163],{"className":2161},[622,2162],"vbox",[572,2164,2167],{"className":2165},[2166],"thinbox",[572,2168,2171,2175,2186],{"className":2169},[2170],"rlap",[572,2172],{"className":2173,"style":2174},[617],"height:0.8889em;vertical-align:-0.1944em;",[572,2176,2179],{"className":2177},[2178],"inner",[572,2180,2182],{"className":2181},[622],[572,2183,2185],{"className":2184},[848],"",[572,2187],{"className":2188},[2189],"fix",[572,2191],{"className":2192},[843,2193],"nobreak",[572,2195,766],{"className":2196},[848],[572,2198],{"className":2199,"style":844},[843],[572,2201,2203,2206],{"className":2202},[613],[572,2204],{"className":2205,"style":1228},[617],[572,2207,1468],{"className":2208},[622],[1738,2210,2211,2214],{},[1753,2212,2213],{},"Sekantenverfahren",[1753,2215,2216],{},[572,2217,2219,2256],{"className":2218},[575],[572,2220,2222],{"className":2221},[579],[581,2223,2224],{"xmlns":583},[585,2225,2226,2253],{},[588,2227,2228,2230,2232,2248,2250],{},[594,2229,564],{},[697,2231,766],{},[1443,2233,2234,2246],{},[588,2235,2236,2238,2240],{},[1005,2237,1007],{},[697,2239,1003],{},[2241,2242,2243],"msqrt",{},[1005,2244,2245],{},"5",[1005,2247,1693],{},[697,2249,1907],{},[1005,2251,2252],{},"1,618",[601,2254,2255],{"encoding":603},"p = \\frac{1 + \\sqrt{5}}{2} \\approx 1{,}618",[572,2257,2259,2277,2430],{"className":2258,"ariaHidden":609},[608],[572,2260,2262,2265,2268,2271,2274],{"className":2261},[613],[572,2263],{"className":2264,"style":976},[617],[572,2266,564],{"className":2267},[622,626],[572,2269],{"className":2270,"style":844},[843],[572,2272,766],{"className":2273},[848],[572,2275],{"className":2276,"style":844},[843],[572,2278,2280,2284,2421,2424,2427],{"className":2279},[613],[572,2281],{"className":2282,"style":2283},[617],"height:1.383em;vertical-align:-0.345em;",[572,2285,2287,2290,2418],{"className":2286},[622],[572,2288],{"className":2289},[1488,1489],[572,2291,2293],{"className":2292},[1443],[572,2294,2296,2410],{"className":2295},[634,635],[572,2297,2299,2407],{"className":2298},[639],[572,2300,2303,2317,2325],{"className":2301,"style":2302},[643],"height:1.038em;",[572,2304,2305,2308],{"style":1505},[572,2306],{"className":2307,"style":1509},[651],[572,2309,2311],{"className":2310},[656,657,658,659],[572,2312,2314],{"className":2313},[622,659],[572,2315,1693],{"className":2316},[622,659],[572,2318,2319,2322],{"style":1564},[572,2320],{"className":2321,"style":1509},[651],[572,2323],{"className":2324,"style":1572},[1571],[572,2326,2328,2331],{"style":2327},"top:-3.399em;",[572,2329],{"className":2330,"style":1509},[651],[572,2332,2334],{"className":2333},[656,657,658,659],[572,2335,2337,2340,2343],{"className":2336},[622,659],[572,2338,1007],{"className":2339},[622,659],[572,2341,1003],{"className":2342},[743,659],[572,2344,2347],{"className":2345},[622,2346,659],"sqrt",[572,2348,2350,2398],{"className":2349},[634,635],[572,2351,2353,2395],{"className":2352},[639],[572,2354,2357,2372],{"className":2355,"style":2356},[643],"height:0.9128em;",[572,2358,2362,2365],{"className":2359,"style":2361},[2360],"svg-align","top:-3em;",[572,2363],{"className":2364,"style":1509},[651],[572,2366,2369],{"className":2367,"style":2368},[622,659],"padding-left:0.833em;",[572,2370,2245],{"className":2371},[622,659],[572,2373,2375,2378],{"style":2374},"top:-2.8728em;",[572,2376],{"className":2377,"style":1509},[651],[572,2379,2383],{"className":2380,"style":2382},[2381,659],"hide-tail","min-width:0.853em;height:1.08em;",[2384,2385,2391],"svg",{"xmlns":2386,"width":2387,"height":2388,"viewBox":2389,"preserveAspectRatio":2390},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.08em","0 0 400000 1080","xMinYMin slice",[2392,2393],"path",{"d":2394},"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 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bei einfacher Nullstelle",[564,2511,2512,2513,2541],{},"Aus drei aufeinanderfolgenden Fehlern lässt sich ",[572,2514,2516,2529],{"className":2515},[575],[572,2517,2519],{"className":2518},[579],[581,2520,2521],{"xmlns":583},[585,2522,2523,2527],{},[588,2524,2525],{},[594,2526,564],{},[601,2528,564],{"encoding":603},[572,2530,2532],{"className":2531,"ariaHidden":609},[608],[572,2533,2535,2538],{"className":2534},[613],[572,2536],{"className":2537,"style":976},[617],[572,2539,564],{"className":2540},[622,626]," schätzen:",[572,2543,2546],{"className":2544},[2545],"katex-display",[572,2547,2549,2630],{"className":2548},[575],[572,2550,2552],{"className":2551},[579],[581,2553,2555],{"xmlns":583,"display":2554},"block",[585,2556,2557,2627],{},[588,2558,2559,2561,2563],{},[594,2560,564],{},[697,2562,1907],{},[1443,2564,2565,2597],{},[588,2566,2567,2570,2572,2574,2586,2589,2595],{},[594,2568,2569],{},"ln",[697,2571,1340],{},[697,2573,1921],{"stretchy":1910},[591,2575,2576,2578],{},[594,2577,761],{},[588,2579,2580,2582,2584],{},[594,2581,599],{},[697,2583,1003],{},[1005,2585,1007],{},[594,2587,2588],{"mathvariant":769},"\u002F",[591,2590,2591,2593],{},[594,2592,761],{},[594,2594,599],{},[697,2596,1930],{"stretchy":1910},[588,2598,2599,2601,2603,2605,2611,2613,2625],{},[594,2600,2569],{},[697,2602,1340],{},[697,2604,1921],{"stretchy":1910},[591,2606,2607,2609],{},[594,2608,761],{},[594,2610,599],{},[594,2612,2588],{"mathvariant":769},[591,2614,2615,2617],{},[594,2616,761],{},[588,2618,2619,2621,2623],{},[594,2620,599],{},[697,2622,779],{},[1005,2624,1007],{},[697,2626,1930],{"stretchy":1910},[601,2628,2629],{"encoding":603},"p \\approx \\frac{\\ln(e_{k+1} \u002F e_k)}{\\ln(e_k \u002F e_{k-1})}",[572,2631,2633,2652],{"className":2632,"ariaHidden":609},[608],[572,2634,2636,2640,2643,2646,2649],{"className":2635},[613],[572,2637],{"className":2638,"style":2639},[617],"height:0.6776em;vertical-align:-0.1944em;",[572,2641,564],{"className":2642},[622,626],[572,2644],{"className":2645,"style":844},[843],[572,2647,1907],{"className":2648},[848],[572,2650],{"className":2651,"style":844},[843],[572,2653,2655,2659],{"className":2654},[613],[572,2656],{"className":2657,"style":2658},[617],"height:2.363em;vertical-align:-0.936em;",[572,2660,2662,2665,2918],{"className":2661},[622],[572,2663],{"className":2664},[1488,1489],[572,2666,2668],{"className":2667},[1443],[572,2669,2671,2909],{"className":2670},[634,635],[572,2672,2674,2906],{"className":2673},[639],[572,2675,2678,2788,2796],{"className":2676,"style":2677},[643],"height:1.427em;",[572,2679,2681,2684],{"style":2680},"top:-2.314em;",[572,2682],{"className":2683,"style":1509},[651],[572,2685,2687,2690,2693,2733,2736,2785],{"className":2686},[622],[572,2688,2569],{"className":2689},[1368],[572,2691,1921],{"className":2692},[1488],[572,2694,2696,2699],{"className":2695},[622],[572,2697,761],{"className":2698},[622,626],[572,2700,2702],{"className":2701},[630],[572,2703,2705,2725],{"className":2704},[634,635],[572,2706,2708,2722],{"className":2707},[639],[572,2709,2711],{"className":2710,"style":644},[643],[572,2712,2713,2716],{"style":647},[572,2714],{"className":2715,"style":652},[651],[572,2717,2719],{"className":2718},[656,657,658,659],[572,2720,599],{"className":2721,"style":663},[622,626,659],[572,2723,668],{"className":2724},[667],[572,2726,2728],{"className":2727},[639],[572,2729,2731],{"className":2730,"style":675},[643],[572,2732],{},[572,2734,2588],{"className":2735},[622],[572,2737,2739,2742],{"className":2738},[622],[572,2740,761],{"className":2741},[622,626],[572,2743,2745],{"className":2744},[630],[572,2746,2748,2777],{"className":2747},[634,635],[572,2749,2751,2774],{"className":2750},[639],[572,2752,2754],{"className":2753,"style":644},[643],[572,2755,2756,2759],{"style":647},[572,2757],{"className":2758,"style":652},[651],[572,2760,2762],{"className":2761},[656,657,658,659],[572,2763,2765,2768,2771],{"className":2764},[622,659],[572,2766,599],{"className":2767,"style":663},[622,626,659],[572,2769,779],{"className":2770},[743,659],[572,2772,1007],{"className":2773},[622,659],[572,2775,668],{"className":2776},[667],[572,2778,2780],{"className":2779},[639],[572,2781,2783],{"className":2782,"style":1087},[643],[572,2784],{},[572,2786,1930],{"className":2787},[1650],[572,2789,2790,2793],{"style":1564},[572,2791],{"className":2792,"style":1509},[651],[572,2794],{"className":2795,"style":1572},[1571],[572,2797,2799,2802],{"style":2798},"top:-3.677em;",[572,2800],{"className":2801,"style":1509},[651],[572,2803,2805,2808,2811,2860,2863,2903],{"className":2804},[622],[572,2806,2569],{"className":2807},[1368],[572,2809,1921],{"className":2810},[1488],[572,2812,2814,2817],{"className":2813},[622],[572,2815,761],{"className":2816},[622,626],[572,2818,2820],{"className":2819},[630],[572,2821,2823,2852],{"className":2822},[634,635],[572,2824,2826,2849],{"className":2825},[639],[572,2827,2829],{"className":2828,"style":644},[643],[572,2830,2831,2834],{"style":647},[572,2832],{"className":2833,"style":652},[651],[572,2835,2837],{"className":2836},[656,657,658,659],[572,2838,2840,2843,2846],{"className":2839},[622,659],[572,2841,599],{"className":2842,"style":663},[622,626,659],[572,2844,1003],{"className":2845},[743,659],[572,2847,1007],{"className":2848},[622,659],[572,2850,668],{"className":2851},[667],[572,2853,2855],{"className":2854},[639],[572,2856,2858],{"className":2857,"style":1087},[643],[572,2859],{},[572,2861,2588],{"className":2862},[622],[572,2864,2866,2869],{"className":2865},[622],[572,2867,761],{"className":2868},[622,626],[572,2870,2872],{"className":2871},[630],[572,2873,2875,2895],{"className":2874},[634,635],[572,2876,2878,2892],{"className":2877},[639],[572,2879,2881],{"className":2880,"style":644},[643],[572,2882,2883,2886],{"style":647},[572,2884],{"className":2885,"style":652},[651],[572,2887,2889],{"className":2888},[656,657,658,659],[572,2890,599],{"className":2891,"style":663},[622,626,659],[572,2893,668],{"className":2894},[667],[572,2896,2898],{"className":2897},[639],[572,2899,2901],{"className":2900,"style":675},[643],[572,2902],{},[572,2904,1930],{"className":2905},[1650],[572,2907,668],{"className":2908},[667],[572,2910,2912],{"className":2911},[639],[572,2913,2916],{"className":2914,"style":2915},[643],"height:0.936em;",[572,2917],{},[572,2919],{"className":2920},[1650,1489],[564,2922,2923],{},"Die Ordnung gilt asymptotisch, also nahe am Grenzwert. Weit weg vom Ziel kann ein Verfahren hoher Ordnung langsam sein oder gar nicht konvergieren.",[559,2925,2927],{"id":2926},"beispiele","Beispiele",[564,2929,2930,2931,3036,3037,3416,3417,3510],{},"Newton-Verfahren für ",[572,2932,2934,2960],{"className":2933},[575],[572,2935,2937],{"className":2936},[579],[581,2938,2939],{"xmlns":583},[585,2940,2941,2957],{},[588,2942,2943,2949,2951,2953,2955],{},[692,2944,2945,2947],{},[594,2946,596],{},[1005,2948,1693],{},[697,2950,779],{},[1005,2952,1693],{},[697,2954,766],{},[1005,2956,1468],{},[601,2958,2959],{"encoding":603},"x^2 - 2 = 0",[572,2961,2963,3009,3027],{"className":2962,"ariaHidden":609},[608],[572,2964,2966,2970,3000,3003,3006],{"className":2965},[613],[572,2967],{"className":2968,"style":2969},[617],"height:0.8974em;vertical-align:-0.0833em;",[572,2971,2973,2976],{"className":2972},[622],[572,2974,596],{"className":2975},[622,626],[572,2977,2979],{"className":2978},[630],[572,2980,2982],{"className":2981},[634],[572,2983,2985],{"className":2984},[639],[572,2986,2989],{"className":2987,"style":2988},[643],"height:0.8141em;",[572,2990,2991,2994],{"style":733},[572,2992],{"className":2993,"style":652},[651],[572,2995,2997],{"className":2996},[656,657,658,659],[572,2998,1693],{"className":2999},[622,659],[572,3001],{"className":3002,"style":905},[843],[572,3004,779],{"className":3005},[743],[572,3007],{"className":3008,"style":905},[843],[572,3010,3012,3015,3018,3021,3024],{"className":3011},[613],[572,3013],{"className":3014,"style":1228},[617],[572,3016,1693],{"className":3017},[622],[572,3019],{"className":3020,"style":844},[843],[572,3022,766],{"className":3023},[848],[572,3025],{"className":3026,"style":844},[843],[572,3028,3030,3033],{"className":3029},[613],[572,3031],{"className":3032,"style":1228},[617],[572,3034,1468],{"className":3035},[622],", also ",[572,3038,3040,3096],{"className":3039},[575],[572,3041,3043],{"className":3042},[579],[581,3044,3045],{"xmlns":583},[585,3046,3047,3093],{},[588,3048,3049,3061,3063,3069],{},[591,3050,3051,3053],{},[594,3052,596],{},[588,3054,3055,3057,3059],{},[594,3056,599],{},[697,3058,1003],{},[1005,3060,1007],{},[697,3062,766],{},[1443,3064,3065,3067],{},[1005,3066,1007],{},[1005,3068,1693],{},[588,3070,3071,3073,3079,3081,3091],{},[697,3072,1921],{"fence":609},[591,3074,3075,3077],{},[594,3076,596],{},[594,3078,599],{},[697,3080,1003],{},[1443,3082,3083,3085],{},[1005,3084,1693],{},[591,3086,3087,3089],{},[594,3088,596],{},[594,3090,599],{},[697,3092,1930],{"fence":609},[601,3094,3095],{"encoding":603},"x_{k+1} = \\frac{1}{2}\\left(x_k + 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ab ",[572,3418,3420,3442],{"className":3419},[575],[572,3421,3423],{"className":3422},[579],[581,3424,3425],{"xmlns":583},[585,3426,3427,3439],{},[588,3428,3429,3435,3437],{},[591,3430,3431,3433],{},[594,3432,596],{},[1005,3434,1468],{},[697,3436,766],{},[1005,3438,1007],{},[601,3440,3441],{"encoding":603},"x_0 = 1",[572,3443,3445,3501],{"className":3444,"ariaHidden":609},[608],[572,3446,3448,3451,3492,3495,3498],{"className":3447},[613],[572,3449],{"className":3450,"style":618},[617],[572,3452,3454,3457],{"className":3453},[622],[572,3455,596],{"className":3456},[622,626],[572,3458,3460],{"className":3459},[630],[572,3461,3463,3484],{"className":3462},[634,635],[572,3464,3466,3481],{"className":3465},[639],[572,3467,3470],{"className":3468,"style":3469},[643],"height:0.3011em;",[572,3471,3472,3475],{"style":647},[572,3473],{"className":3474,"style":652},[651],[572,3476,3478],{"className":3477},[656,657,658,659],[572,3479,1468],{"className":3480},[622,659],[572,3482,668],{"className":3483},[667],[572,3485,3487],{"className":3486},[639],[572,3488,3490],{"className":3489,"style":675},[643],[572,3491],{},[572,3493],{"className":3494,"style":844},[843],[572,3496,766],{"className":3497},[848],[572,3499],{"className":3500,"style":844},[843],[572,3502,3504,3507],{"className":3503},[613],[572,3505],{"className":3506,"style":1228},[617],[572,3508,1007],{"className":3509},[622],":",[1732,3512,3513,3692],{},[1735,3514,3515],{},[1738,3516,3517,3548,3619],{},[1741,3518,3519],{},[572,3520,3522,3535],{"className":3521},[575],[572,3523,3525],{"className":3524},[579],[581,3526,3527],{"xmlns":583},[585,3528,3529,3533],{},[588,3530,3531],{},[594,3532,599],{},[601,3534,599],{"encoding":603},[572,3536,3538],{"className":3537,"ariaHidden":609},[608],[572,3539,3541,3545],{"className":3540},[613],[572,3542],{"className":3543,"style":3544},[617],"height:0.6944em;",[572,3546,599],{"className":3547,"style":663},[622,626],[1741,3549,3550],{},[572,3551,3553,3570],{"className":3552},[575],[572,3554,3556],{"className":3555},[579],[581,3557,3558],{"xmlns":583},[585,3559,3560,3568],{},[588,3561,3562],{},[591,3563,3564,3566],{},[594,3565,596],{},[594,3567,599],{},[601,3569,604],{"encoding":603},[572,3571,3573],{"className":3572,"ariaHidden":609},[608],[572,3574,3576,3579],{"className":3575},[613],[572,3577],{"className":3578,"style":618},[617],[572,3580,3582,3585],{"className":3581},[622],[572,3583,596],{"className":3584},[622,626],[572,3586,3588],{"className":3587},[630],[572,3589,3591,3611],{"className":3590},[634,635],[572,3592,3594,3608],{"className":3593},[639],[572,3595,3597],{"className":3596,"style":644},[643],[572,3598,3599,3602],{"style":647},[572,3600],{"className":3601,"style":652},[651],[572,3603,3605],{"className":3604},[656,657,658,659],[572,3606,599],{"className":3607,"style":663},[622,626,659],[572,3609,668],{"className":3610},[667],[572,3612,3614],{"className":3613},[639],[572,3615,3617],{"className":3616,"style":675},[643],[572,3618],{},[1741,3620,3621,3622],{},"Fehler ",[572,3623,3625,3643],{"className":3624},[575],[572,3626,3628],{"className":3627},[579],[581,3629,3630],{"xmlns":583},[585,3631,3632,3640],{},[588,3633,3634],{},[591,3635,3636,3638],{},[594,3637,761],{},[594,3639,599],{},[601,3641,3642],{"encoding":603},"e_k",[572,3644,3646],{"className":3645,"ariaHidden":609},[608],[572,3647,3649,3652],{"className":3648},[613],[572,3650],{"className":3651,"style":618},[617],[572,3653,3655,3658],{"className":3654},[622],[572,3656,761],{"className":3657},[622,626],[572,3659,3661],{"className":3660},[630],[572,3662,3664,3684],{"className":3663},[634,635],[572,3665,3667,3681],{"className":3666},[639],[572,3668,3670],{"className":3669,"style":644},[643],[572,3671,3672,3675],{"style":647},[572,3673],{"className":3674,"style":652},[651],[572,3676,3678],{"className":3677},[656,657,658,659],[572,3679,599],{"className":3680,"style":663},[622,626,659],[572,3682,668],{"className":3683},[667],[572,3685,3687],{"className":3686},[639],[572,3688,3690],{"className":3689,"style":675},[643],[572,3691],{},[1748,3693,3694,3704,3846],{},[1738,3695,3696,3698,3701],{},[1753,3697,1007],{},[1753,3699,3700],{},"1,5",[1753,3702,3703],{},"0,0858",[1738,3705,3706,3708,3843],{},[1753,3707,1693],{},[1753,3709,3710],{},[572,3711,3713,3738],{"className":3712},[575],[572,3714,3716],{"className":3715},[579],[581,3717,3718],{"xmlns":583},[585,3719,3720,3735],{},[588,3721,3722,3730,3732],{},[1443,3723,3724,3727],{},[1005,3725,3726],{},"17",[1005,3728,3729],{},"12",[697,3731,1907],{},[1005,3733,3734],{},"1,416667",[601,3736,3737],{"encoding":603},"\\frac{17}{12} \\approx 1{,}416667",[572,3739,3741,3824],{"className":3740,"ariaHidden":609},[608],[572,3742,3744,3747,3815,3818,3821],{"className":3743},[613],[572,3745],{"className":3746,"style":1811},[617],[572,3748,3750,3753,3812],{"className":3749},[622],[572,3751],{"className":3752},[1488,1489],[572,3754,3756],{"className":3755},[1443],[572,3757,3759,3804],{"className":3758},[634,635],[572,3760,3762,3801],{"className":3761},[639],[572,3763,3765,3779,3787],{"className":3764,"style":1830},[643],[572,3766,3767,3770],{"style":1505},[572,3768],{"className":3769,"style":1509},[651],[572,3771,3773],{"className":3772},[656,657,658,659],[572,3774,3776],{"className":3775},[622,659],[572,3777,3729],{"className":3778},[622,659],[572,3780,3781,3784],{"style":1564},[572,3782],{"className":3783,"style":1509},[651],[572,3785],{"className":3786,"style":1572},[1571],[572,3788,3789,3792],{"style":1855},[572,3790],{"className":3791,"style":1509},[651],[572,3793,3795],{"className":3794},[656,657,658,659],[572,3796,3798],{"className":3797},[622,659],[572,3799,3726],{"className":3800},[622,659],[572,3802,668],{"className":3803},[667],[572,3805,3807],{"className":3806},[639],[572,3808,3810],{"className":3809,"style":1877},[643],[572,3811],{},[572,3813],{"className":3814},[1650,1489],[572,3816],{"className":3817,"style":844},[843],[572,3819,1907],{"className":3820},[848],[572,3822],{"className":3823,"style":844},[843],[572,3825,3827,3830,3833,3839],{"className":3826},[613],[572,3828],{"className":3829,"style":2436},[617],[572,3831,1007],{"className":3832},[622],[572,3834,3836],{"className":3835},[622],[572,3837,2447],{"className":3838},[2446],[572,3840,3842],{"className":3841},[622],"416667",[1753,3844,3845],{},"0,0025",[1738,3847,3848,3851,3986],{},[1753,3849,3850],{},"3",[1753,3852,3853],{},[572,3854,3856,3881],{"className":3855},[575],[572,3857,3859],{"className":3858},[579],[581,3860,3861],{"xmlns":583},[585,3862,3863,3878],{},[588,3864,3865,3873,3875],{},[1443,3866,3867,3870],{},[1005,3868,3869],{},"577",[1005,3871,3872],{},"408",[697,3874,1907],{},[1005,3876,3877],{},"1,414216",[601,3879,3880],{"encoding":603},"\\frac{577}{408} \\approx 1{,}414216",[572,3882,3884,3967],{"className":3883,"ariaHidden":609},[608],[572,3885,3887,3890,3958,3961,3964],{"className":3886},[613],[572,3888],{"className":3889,"style":1811},[617],[572,3891,3893,3896,3955],{"className":3892},[622],[572,3894],{"className":3895},[1488,1489],[572,3897,3899],{"className":3898},[1443],[572,3900,3902,3947],{"className":3901},[634,635],[572,3903,3905,3944],{"className":3904},[639],[572,3906,3908,3922,3930],{"className":3907,"style":1830},[643],[572,3909,3910,3913],{"style":1505},[572,3911],{"className":3912,"style":1509},[651],[572,3914,3916],{"className":3915},[656,657,658,659],[572,3917,3919],{"className":3918},[622,659],[572,3920,3872],{"className":3921},[622,659],[572,3923,3924,3927],{"style":1564},[572,3925],{"className":3926,"style":1509},[651],[572,3928],{"className":3929,"style":1572},[1571],[572,3931,3932,3935],{"style":1855},[572,3933],{"className":3934,"style":1509},[651],[572,3936,3938],{"className":3937},[656,657,658,659],[572,3939,3941],{"className":3940},[622,659],[572,3942,3869],{"className":3943},[622,659],[572,3945,668],{"className":3946},[667],[572,3948,3950],{"className":3949},[639],[572,3951,3953],{"className":3952,"style":1877},[643],[572,3954],{},[572,3956],{"className":3957},[1650,1489],[572,3959],{"className":3960,"style":844},[843],[572,3962,1907],{"className":3963},[848],[572,3965],{"className":3966,"style":844},[843],[572,3968,3970,3973,3976,3982],{"className":3969},[613],[572,3971],{"className":3972,"style":2436},[617],[572,3974,1007],{"className":3975},[622],[572,3977,3979],{"className":3978},[622],[572,3980,2447],{"className":3981},[2446],[572,3983,3985],{"className":3984},[622],"414216",[1753,3987,3988],{},[572,3989,3991,4020],{"className":3990},[575],[572,3992,3994],{"className":3993},[579],[581,3995,3996],{"xmlns":583},[585,3997,3998,4017],{},[588,3999,4000,4003,4006],{},[1005,4001,4002],{},"2,1",[697,4004,4005],{},"⋅",[692,4007,4008,4010],{},[1005,4009,1343],{},[588,4011,4012,4014],{},[697,4013,779],{},[1005,4015,4016],{},"6",[601,4018,4019],{"encoding":603},"2{,}1 \\cdot 10^{-6}",[572,4021,4023,4050],{"className":4022,"ariaHidden":609},[608],[572,4024,4026,4029,4032,4038,4041,4044,4047],{"className":4025},[613],[572,4027],{"className":4028,"style":2436},[617],[572,4030,1693],{"className":4031},[622],[572,4033,4035],{"className":4034},[622],[572,4036,2447],{"className":4037},[2446],[572,4039,1007],{"className":4040},[622],[572,4042],{"className":4043,"style":905},[843],[572,4045,4005],{"className":4046},[743],[572,4048],{"className":4049,"style":905},[843],[572,4051,4053,4056,4059],{"className":4052},[613],[572,4054],{"className":4055,"style":2988},[617],[572,4057,1007],{"className":4058},[622],[572,4060,4062,4065],{"className":4061},[622],[572,4063,1468],{"className":4064},[622],[572,4066,4068],{"className":4067},[630],[572,4069,4071],{"className":4070},[634],[572,4072,4074],{"className":4073},[639],[572,4075,4077],{"className":4076,"style":2988},[643],[572,4078,4079,4082],{"style":733},[572,4080],{"className":4081,"style":652},[651],[572,4083,4085],{"className":4084},[656,657,658,659],[572,4086,4088,4091],{"className":4087},[622,659],[572,4089,779],{"className":4090},[622,659],[572,4092,4016],{"className":4093},[622,659],[564,4095,4096,4097,1232,4167,1232,4237,4307,4308,4370,4371,4945],{},"Die Schätzformel mit ",[572,4098,4100,4118],{"className":4099},[575],[572,4101,4103],{"className":4102},[579],[581,4104,4105],{"xmlns":583},[585,4106,4107,4115],{},[588,4108,4109],{},[591,4110,4111,4113],{},[594,4112,761],{},[1005,4114,1007],{},[601,4116,4117],{"encoding":603},"e_1",[572,4119,4121],{"className":4120,"ariaHidden":609},[608],[572,4122,4124,4127],{"className":4123},[613],[572,4125],{"className":4126,"style":618},[617],[572,4128,4130,4133],{"className":4129},[622],[572,4131,761],{"className":4132},[622,626],[572,4134,4136],{"className":4135},[630],[572,4137,4139,4159],{"className":4138},[634,635],[572,4140,4142,4156],{"className":4141},[639],[572,4143,4145],{"className":4144,"style":3469},[643],[572,4146,4147,4150],{"style":647},[572,4148],{"className":4149,"style":652},[651],[572,4151,4153],{"className":4152},[656,657,658,659],[572,4154,1007],{"className":4155},[622,659],[572,4157,668],{"className":4158},[667],[572,4160,4162],{"className":4161},[639],[572,4163,4165],{"className":4164,"style":675},[643],[572,4166],{},[572,4168,4170,4188],{"className":4169},[575],[572,4171,4173],{"className":4172},[579],[581,4174,4175],{"xmlns":583},[585,4176,4177,4185],{},[588,4178,4179],{},[591,4180,4181,4183],{},[594,4182,761],{},[1005,4184,1693],{},[601,4186,4187],{"encoding":603},"e_2",[572,4189,4191],{"className":4190,"ariaHidden":609},[608],[572,4192,4194,4197],{"className":4193},[613],[572,4195],{"className":4196,"style":618},[617],[572,4198,4200,4203],{"className":4199},[622],[572,4201,761],{"className":4202},[622,626],[572,4204,4206],{"className":4205},[630],[572,4207,4209,4229],{"className":4208},[634,635],[572,4210,4212,4226],{"className":4211},[639],[572,4213,4215],{"className":4214,"style":3469},[643],[572,4216,4217,4220],{"style":647},[572,4218],{"className":4219,"style":652},[651],[572,4221,4223],{"className":4222},[656,657,658,659],[572,4224,1693],{"className":4225},[622,659],[572,4227,668],{"className":4228},[667],[572,4230,4232],{"className":4231},[639],[572,4233,4235],{"className":4234,"style":675},[643],[572,4236],{},[572,4238,4240,4258],{"className":4239},[575],[572,4241,4243],{"className":4242},[579],[581,4244,4245],{"xmlns":583},[585,4246,4247,4255],{},[588,4248,4249],{},[591,4250,4251,4253],{},[594,4252,761],{},[1005,4254,3850],{},[601,4256,4257],{"encoding":603},"e_3",[572,4259,4261],{"className":4260,"ariaHidden":609},[608],[572,4262,4264,4267],{"className":4263},[613],[572,4265],{"className":4266,"style":618},[617],[572,4268,4270,4273],{"className":4269},[622],[572,4271,761],{"className":4272},[622,626],[572,4274,4276],{"className":4275},[630],[572,4277,4279,4299],{"className":4278},[634,635],[572,4280,4282,4296],{"className":4281},[639],[572,4283,4285],{"className":4284,"style":3469},[643],[572,4286,4287,4290],{"style":647},[572,4288],{"className":4289,"style":652},[651],[572,4291,4293],{"className":4292},[656,657,658,659],[572,4294,3850],{"className":4295},[622,659],[572,4297,668],{"className":4298},[667],[572,4300,4302],{"className":4301},[639],[572,4303,4305],{"className":4304,"style":675},[643],[572,4306],{}," ergibt ",[572,4309,4311,4330],{"className":4310},[575],[572,4312,4314],{"className":4313},[579],[581,4315,4316],{"xmlns":583},[585,4317,4318,4327],{},[588,4319,4320,4322,4324],{},[594,4321,564],{},[697,4323,1907],{},[1005,4325,4326],{},"1,98",[601,4328,4329],{"encoding":603},"p \\approx 1{,}98",[572,4331,4333,4351],{"className":4332,"ariaHidden":609},[608],[572,4334,4336,4339,4342,4345,4348],{"className":4335},[613],[572,4337],{"className":4338,"style":2639},[617],[572,4340,564],{"className":4341},[622,626],[572,4343],{"className":4344,"style":844},[843],[572,4346,1907],{"className":4347},[848],[572,4349],{"className":4350,"style":844},[843],[572,4352,4354,4357,4360,4366],{"className":4353},[613],[572,4355],{"className":4356,"style":2436},[617],[572,4358,1007],{"className":4359},[622],[572,4361,4363],{"className":4362},[622],[572,4364,2447],{"className":4365},[2446],[572,4367,4369],{"className":4368},[622],"98",", also quadratische Konvergenz. Die Konstante ist ",[572,4372,4374,4460],{"className":4373},[575],[572,4375,4377],{"className":4376},[579],[581,4378,4379],{"xmlns":583},[585,4380,4381,4457],{},[588,4382,4383,4385,4387,4438,4440,4452,4454],{},[594,4384,1013],{},[697,4386,766],{},[588,4388,4389,4391,4436],{},[697,4390,770],{"fence":609},[1443,4392,4393,4416],{},[588,4394,4395,4406,4408,4414],{},[692,4396,4397,4400],{},[594,4398,4399],{},"f",[588,4401,4402,4404],{},[697,4403,1918],{"mathvariant":769},[697,4405,1918],{"mathvariant":769},[697,4407,1921],{"stretchy":1910},[692,4409,4410,4412],{},[594,4411,596],{},[697,4413,699],{},[697,4415,1930],{"stretchy":1910},[588,4417,4418,4420,4426,4428,4434],{},[1005,4419,1693],{},[692,4421,4422,4424],{},[594,4423,4399],{},[697,4425,1918],{"mathvariant":769,"lspace":1917,"rspace":1917},[697,4427,1921],{"stretchy":1910},[692,4429,4430,4432],{},[594,4431,596],{},[697,4433,699],{},[697,4435,1930],{"stretchy":1910},[697,4437,770],{"fence":609},[697,4439,766],{},[1443,4441,4442,4444],{},[1005,4443,1007],{},[588,4445,4446,4448],{},[1005,4447,1693],{},[2241,4449,4450],{},[1005,4451,1693],{},[697,4453,1907],{},[1005,4455,4456],{},"0,35",[601,4458,4459],{"encoding":603},"C = \\left|\\frac{f''(x^*)}{2 f'(x^*)}\\right| = \\frac{1}{2\\sqrt{2}} \\approx 0{,}35",[572,4461,4463,4481,4793,4926],{"className":4462,"ariaHidden":609},[608],[572,4464,4466,4469,4472,4475,4478],{"className":4465},[613],[572,4467],{"className":4468,"style":1312},[617],[572,4470,1013],{"className":4471,"style":1109},[622,626],[572,4473],{"className":4474,"style":844},[843],[572,4476,766],{"className":4477},[848],[572,4479],{"className":4480,"style":844},[843],[572,4482,4484,4487,4784,4787,4790],{"className":4483},[613],[572,4485],{"className":4486,"style":3170},[617],[572,4488,4490,4537,4747],{"className":4489},[3245],[572,4491,4493],{"className":4492},[1488],[572,4494,4497],{"className":4495},[3254,4496],"mult",[572,4498,4500,4528],{"className":4499},[634,635],[572,4501,4503,4525],{"className":4502},[639],[572,4504,4507],{"className":4505,"style":4506},[643],"height:1.15em;",[572,4508,4510,4514],{"style":4509},"top:-3.15em;",[572,4511],{"className":4512,"style":4513},[651],"height:3.8em;",[572,4515,4517],{"style":4516},"width:0.333em;height:1.8em;",[2384,4518,4522],{"xmlns":2386,"width":4519,"height":4520,"viewBox":4521},"0.333em","1.8em","0 0 333 1800",[2392,4523],{"d":4524},"M145 15 v585 v600 v585 c2.667,10,9.667,15,21,15\nc10,0,16.667,-5,20,-15 v-585 v-600 v-585 c-2.667,-10,-9.667,-15,-21,-15\nc-10,0,-16.667,5,-20,15z M188 15 H145 v585 v600 v585 h43z",[572,4526,668],{"className":4527},[667],[572,4529,4531],{"className":4530},[639],[572,4532,4535],{"className":4533,"style":4534},[643],"height:0.65em;",[572,4536],{},[572,4538,4540,4543,4744],{"className":4539},[622],[572,4541],{"className":4542},[1488,1489],[572,4544,4546],{"className":4545},[1443],[572,4547,4549,4735],{"className":4548},[634,635],[572,4550,4552,4732],{"className":4551},[639],[572,4553,4556,4641,4649],{"className":4554,"style":4555},[643],"height:1.0645em;",[572,4557,4558,4561],{"style":1505},[572,4559],{"className":4560,"style":1509},[651],[572,4562,4564],{"className":4563},[656,657,658,659],[572,4565,4567,4570,4605,4608,4638],{"className":4566},[622,659],[572,4568,1693],{"className":4569},[622,659],[572,4571,4573,4577],{"className":4572},[622,659],[572,4574,4399],{"className":4575,"style":4576},[622,626,659],"margin-right:0.1076em;",[572,4578,4580],{"className":4579},[630],[572,4581,4583],{"className":4582},[634],[572,4584,4586],{"className":4585},[639],[572,4587,4590],{"className":4588,"style":4589},[643],"height:0.6828em;",[572,4591,4593,4596],{"style":4592},"top:-2.786em;margin-right:0.0714em;",[572,4594],{"className":4595,"style":1541},[651],[572,4597,4599],{"className":4598},[656,1545,1546,659],[572,4600,4602],{"className":4601},[622,659],[572,4603,1918],{"className":4604},[622,659],[572,4606,1921],{"className":4607},[1488,659],[572,4609,4611,4614],{"className":4610},[622,659],[572,4612,596],{"className":4613},[622,626,659],[572,4615,4617],{"className":4616},[630],[572,4618,4620],{"className":4619},[634],[572,4621,4623],{"className":4622},[639],[572,4624,4627],{"className":4625,"style":4626},[643],"height:0.6183em;",[572,4628,4629,4632],{"style":4592},[572,4630],{"className":4631,"style":1541},[651],[572,4633,4635],{"className":4634},[656,1545,1546,659],[572,4636,699],{"className":4637},[743,659],[572,4639,1930],{"className":4640},[1650,659],[572,4642,4643,4646],{"style":1564},[572,4644],{"className":4645,"style":1509},[651],[572,4647],{"className":4648,"style":1572},[1571],[572,4650,4652,4655],{"style":4651},"top:-3.485em;",[572,4653],{"className":4654,"style":1509},[651],[572,4656,4658],{"className":4657},[656,657,658,659],[572,4659,4661,4696,4699,4729],{"className":4660},[622,659],[572,4662,4664,4667],{"className":4663},[622,659],[572,4665,4399],{"className":4666,"style":4576},[622,626,659],[572,4668,4670],{"className":4669},[630],[572,4671,4673],{"className":4672},[634],[572,4674,4676],{"className":4675},[639],[572,4677,4680],{"className":4678,"style":4679},[643],"height:0.8278em;",[572,4681,4683,4686],{"style":4682},"top:-2.931em;margin-right:0.0714em;",[572,4684],{"className":4685,"style":1541},[651],[572,4687,4689],{"className":4688},[656,1545,1546,659],[572,4690,4692],{"className":4691},[622,659],[572,4693,4695],{"className":4694},[622,659],"′′",[572,4697,1921],{"className":4698},[1488,659],[572,4700,4702,4705],{"className":4701},[622,659],[572,4703,596],{"className":4704},[622,626,659],[572,4706,4708],{"className":4707},[630],[572,4709,4711],{"className":4710},[634],[572,4712,4714],{"className":4713},[639],[572,4715,4718],{"className":4716,"style":4717},[643],"height:0.7633em;",[572,4719,4720,4723],{"style":4682},[572,4721],{"className":4722,"style":1541},[651],[572,4724,4726],{"className":4725},[656,1545,1546,659],[572,4727,699],{"className":4728},[743,659],[572,4730,1930],{"className":4731},[1650,659],[572,4733,668],{"className":4734},[667],[572,4736,4738],{"className":4737},[639],[572,4739,4742],{"className":4740,"style":4741},[643],"height:0.52em;",[572,4743],{},[572,4745],{"className":4746},[1650,1489],[572,4748,4750],{"className":4749},[1650],[572,4751,4753],{"className":4752},[3254,4496],[572,4754,4756,4776],{"className":4755},[634,635],[572,4757,4759,4773],{"className":4758},[639],[572,4760,4762],{"className":4761,"style":4506},[643],[572,4763,4764,4767],{"style":4509},[572,4765],{"className":4766,"style":4513},[651],[572,4768,4769],{"style":4516},[2384,4770,4771],{"xmlns":2386,"width":4519,"height":4520,"viewBox":4521},[2392,4772],{"d":4524},[572,4774,668],{"className":4775},[667],[572,4777,4779],{"className":4778},[639],[572,4780,4782],{"className":4781,"style":4534},[643],[572,4783],{},[572,4785],{"className":4786,"style":844},[843],[572,4788,766],{"className":4789},[848],[572,4791],{"className":4792,"style":844},[843],[572,4794,4796,4800,4917,4920,4923],{"className":4795},[613],[572,4797],{"className":4798,"style":4799},[617],"height:1.3831em;vertical-align:-0.538em;",[572,4801,4803,4806,4914],{"className":4802},[622],[572,4804],{"className":4805},[1488,1489],[572,4807,4809],{"className":4808},[1443],[572,4810,4812,4905],{"className":4811},[634,635],[572,4813,4815,4902],{"className":4814},[639],[572,4816,4818,4880,4888],{"className":4817,"style":1830},[643],[572,4819,4821,4824],{"style":4820},"top:-2.551em;",[572,4822],{"className":4823,"style":1509},[651],[572,4825,4827],{"className":4826},[656,657,658,659],[572,4828,4830,4833],{"className":4829},[622,659],[572,4831,1693],{"className":4832},[622,659],[572,4834,4836],{"className":4835},[622,2346,659],[572,4837,4839,4872],{"className":4838},[634,635],[572,4840,4842,4869],{"className":4841},[639],[572,4843,4845,4857],{"className":4844,"style":2356},[643],[572,4846,4848,4851],{"className":4847,"style":2361},[2360],[572,4849],{"className":4850,"style":1509},[651],[572,4852,4854],{"className":4853,"style":2368},[622,659],[572,4855,1693],{"className":4856},[622,659],[572,4858,4859,4862],{"style":2374},[572,4860],{"className":4861,"style":1509},[651],[572,4863,4865],{"className":4864,"style":2382},[2381,659],[2384,4866,4867],{"xmlns":2386,"width":2387,"height":2388,"viewBox":2389,"preserveAspectRatio":2390},[2392,4868],{"d":2394},[572,4870,668],{"className":4871},[667],[572,4873,4875],{"className":4874},[639],[572,4876,4878],{"className":4877,"style":2404},[643],[572,4879],{},[572,4881,4882,4885],{"style":1564},[572,4883],{"className":4884,"style":1509},[651],[572,4886],{"className":4887,"style":1572},[1571],[572,4889,4890,4893],{"style":1855},[572,4891],{"className":4892,"style":1509},[651],[572,4894,4896],{"className":4895},[656,657,658,659],[572,4897,4899],{"className":4898},[622,659],[572,4900,1007],{"className":4901},[622,659],[572,4903,668],{"className":4904},[667],[572,4906,4908],{"className":4907},[639],[572,4909,4912],{"className":4910,"style":4911},[643],"height:0.538em;",[572,4913],{},[572,4915],{"className":4916},[1650,1489],[572,4918],{"className":4919,"style":844},[843],[572,4921,1907],{"className":4922},[848],[572,4924],{"className":4925,"style":844},[843],[572,4927,4929,4932,4935,4941],{"className":4928},[613],[572,4930],{"className":4931,"style":2436},[617],[572,4933,1468],{"className":4934},[622],[572,4936,4938],{"className":4937},[622],[572,4939,2447],{"className":4940},[2446],[572,4942,4944],{"className":4943},[622],"35",".",[564,4947,4948,4949,5191,5192,5220,5221,5498,5499,5560,5561,1423],{},"Die Fixpunktiteration ",[572,4950,4952,4992],{"className":4951},[575],[572,4953,4955],{"className":4954},[579],[581,4956,4957],{"xmlns":583},[585,4958,4959,4989],{},[588,4960,4961,4973,4975,4985,4987],{},[591,4962,4963,4965],{},[594,4964,596],{},[588,4966,4967,4969,4971],{},[594,4968,599],{},[697,4970,1003],{},[1005,4972,1007],{},[697,4974,766],{},[1443,4976,4977,4983],{},[591,4978,4979,4981],{},[594,4980,596],{},[594,4982,599],{},[1005,4984,1693],{},[697,4986,1003],{},[1005,4988,1007],{},[601,4990,4991],{"encoding":603},"x_{k+1} = \\frac{x_k}{2} + 1",[572,4993,4995,5059,5182],{"className":4994,"ariaHidden":609},[608],[572,4996,4998,5001,5050,5053,5056],{"className":4997},[613],[572,4999],{"className":5000,"style":3105},[617],[572,5002,5004,5007],{"className":5003},[622],[572,5005,596],{"className":5006},[622,626],[572,5008,5010],{"className":5009},[630],[572,5011,5013,5042],{"className":5012},[634,635],[572,5014,5016,5039],{"className":5015},[639],[572,5017,5019],{"className":5018,"style":644},[643],[572,5020,5021,5024],{"style":647},[572,5022],{"className":5023,"style":652},[651],[572,5025,5027],{"className":5026},[656,657,658,659],[572,5028,5030,5033,5036],{"className":5029},[622,659],[572,5031,599],{"className":5032,"style":663},[622,626,659],[572,5034,1003],{"className":5035},[743,659],[572,5037,1007],{"className":5038},[622,659],[572,5040,668],{"className":5041},[667],[572,5043,5045],{"className":5044},[639],[572,5046,5048],{"className":5047,"style":1087},[643],[572,5049],{},[572,5051],{"className":5052,"style":844},[843],[572,5054,766],{"className":5055},[848],[572,5057],{"className":5058,"style":844},[843],[572,5060,5062,5066,5173,5176,5179],{"className":5061},[613],[572,5063],{"className":5064,"style":5065},[617],"height:1.0623em;vertical-align:-0.345em;",[572,5067,5069,5072,5170],{"className":5068},[622],[572,5070],{"className":5071},[1488,1489],[572,5073,5075],{"className":5074},[1443],[572,5076,5078,5162],{"className":5077},[634,635],[572,5079,5081,5159],{"className":5080},[639],[572,5082,5085,5099,5107],{"className":5083,"style":5084},[643],"height:0.7173em;",[572,5086,5087,5090],{"style":1505},[572,5088],{"className":5089,"style":1509},[651],[572,5091,5093],{"className":5092},[656,657,658,659],[572,5094,5096],{"className":5095},[622,659],[572,5097,1693],{"className":5098},[622,659],[572,5100,5101,5104],{"style":1564},[572,5102],{"className":5103,"style":1509},[651],[572,5105],{"className":5106,"style":1572},[1571],[572,5108,5110,5113],{"style":5109},"top:-3.4159em;",[572,5111],{"className":5112,"style":1509},[651],[572,5114,5116],{"className":5115},[656,657,658,659],[572,5117,5119],{"className":5118},[622,659],[572,5120,5122,5125],{"className":5121},[622,659],[572,5123,596],{"className":5124},[622,626,659],[572,5126,5128],{"className":5127},[630],[572,5129,5131,5151],{"className":5130},[634,635],[572,5132,5134,5148],{"className":5133},[639],[572,5135,5137],{"className":5136,"style":1534},[643],[572,5138,5139,5142],{"style":1537},[572,5140],{"className":5141,"style":1541},[651],[572,5143,5145],{"className":5144},[656,1545,1546,659],[572,5146,599],{"className":5147,"style":663},[622,626,659],[572,5149,668],{"className":5150},[667],[572,5152,5154],{"className":5153},[639],[572,5155,5157],{"className":5156,"style":1559},[643],[572,5158],{},[572,5160,668],{"className":5161},[667],[572,5163,5165],{"className":5164},[639],[572,5166,5168],{"className":5167,"style":1877},[643],[572,5169],{},[572,5171],{"className":5172},[1650,1489],[572,5174],{"className":5175,"style":905},[843],[572,5177,1003],{"className":5178},[743],[572,5180],{"className":5181,"style":905},[843],[572,5183,5185,5188],{"className":5184},[613],[572,5186],{"className":5187,"style":1228},[617],[572,5189,1007],{"className":5190},[622]," hat den Fixpunkt ",[572,5193,5195,5208],{"className":5194},[575],[572,5196,5198],{"className":5197},[579],[581,5199,5200],{"xmlns":583},[585,5201,5202,5206],{},[588,5203,5204],{},[1005,5205,1693],{},[601,5207,1693],{"encoding":603},[572,5209,5211],{"className":5210,"ariaHidden":609},[608],[572,5212,5214,5217],{"className":5213},[613],[572,5215],{"className":5216,"style":1228},[617],[572,5218,1693],{"className":5219},[622],", und es gilt exakt ",[572,5222,5224,5274],{"className":5223},[575],[572,5225,5227],{"className":5226},[579],[581,5228,5229],{"xmlns":583},[585,5230,5231,5271],{},[588,5232,5233,5245,5247,5249,5251,5257,5259,5265,5267,5269],{},[591,5234,5235,5237],{},[594,5236,596],{},[588,5238,5239,5241,5243],{},[594,5240,599],{},[697,5242,1003],{},[1005,5244,1007],{},[697,5246,779],{},[1005,5248,1693],{},[697,5250,766],{},[1443,5252,5253,5255],{},[1005,5254,1007],{},[1005,5256,1693],{},[697,5258,1921],{"stretchy":1910},[591,5260,5261,5263],{},[594,5262,596],{},[594,5264,599],{},[697,5266,779],{},[1005,5268,1693],{},[697,5270,1930],{"stretchy":1910},[601,5272,5273],{"encoding":603},"x_{k+1} - 2 = \\frac{1}{2}(x_k - 2)",[572,5275,5277,5342,5360,5486],{"className":5276,"ariaHidden":609},[608],[572,5278,5280,5284,5333,5336,5339],{"className":5279},[613],[572,5281],{"className":5282,"style":5283},[617],"height:0.7917em;vertical-align:-0.2083em;",[572,5285,5287,5290],{"className":5286},[622],[572,5288,596],{"className":5289},[622,626],[572,5291,5293],{"className":5292},[630],[572,5294,5296,5325],{"className":5295},[634,635],[572,5297,5299,5322],{"className":5298},[639],[572,5300,5302],{"className":5301,"style":644},[643],[572,5303,5304,5307],{"style":647},[572,5305],{"className":5306,"style":652},[651],[572,5308,5310],{"className":5309},[656,657,658,659],[572,5311,5313,5316,5319],{"className":5312},[622,659],[572,5314,599],{"className":5315,"style":663},[622,626,659],[572,5317,1003],{"className":5318},[743,659],[572,5320,1007],{"className":5321},[622,659],[572,5323,668],{"className":5324},[667],[572,5326,5328],{"className":5327},[639],[572,5329,5331],{"className":5330,"style":1087},[643],[572,5332],{},[572,5334],{"className":5335,"style":905},[843],[572,5337,779],{"className":5338},[743],[572,5340],{"className":5341,"style":905},[843],[572,5343,5345,5348,5351,5354,5357],{"className":5344},[613],[572,5346],{"className":5347,"style":1228},[617],[572,5349,1693],{"className":5350},[622],[572,5352],{"className":5353,"style":844},[843],[572,5355,766],{"className":5356},[848],[572,5358],{"className":5359,"style":844},[843],[572,5361,5363,5366,5434,5437,5477,5480,5483],{"className":5362},[613],[572,5364],{"className":5365,"style":1811},[617],[572,5367,5369,5372,5431],{"className":5368},[622],[572,5370],{"className":5371},[1488,1489],[572,5373,5375],{"className":5374},[1443],[572,5376,5378,5423],{"className":5377},[634,635],[572,5379,5381,5420],{"className":5380},[639],[572,5382,5384,5398,5406],{"className":5383,"style":1830},[643],[572,5385,5386,5389],{"style":1505},[572,5387],{"className":5388,"style":1509},[651],[572,5390,5392],{"className":5391},[656,657,658,659],[572,5393,5395],{"className":5394},[622,659],[572,5396,1693],{"className":5397},[622,659],[572,5399,5400,5403],{"style":1564},[572,5401],{"className":5402,"style":1509},[651],[572,5404],{"className":5405,"style":1572},[1571],[572,5407,5408,5411],{"style":1855},[572,5409],{"className":5410,"style":1509},[651],[572,5412,5414],{"className":5413},[656,657,658,659],[572,5415,5417],{"className":5416},[622,659],[572,5418,1007],{"className":5419},[622,659],[572,5421,668],{"className":5422},[667],[572,5424,5426],{"className":5425},[639],[572,5427,5429],{"className":5428,"style":1877},[643],[572,5430],{},[572,5432],{"className":5433},[1650,1489],[572,5435,1921],{"className":5436},[1488],[572,5438,5440,5443],{"className":5439},[622],[572,5441,596],{"className":5442},[622,626],[572,5444,5446],{"className":5445},[630],[572,5447,5449,5469],{"className":5448},[634,635],[572,5450,5452,5466],{"className":5451},[639],[572,5453,5455],{"className":5454,"style":644},[643],[572,5456,5457,5460],{"style":647},[572,5458],{"className":5459,"style":652},[651],[572,5461,5463],{"className":5462},[656,657,658,659],[572,5464,599],{"className":5465,"style":663},[622,626,659],[572,5467,668],{"className":5468},[667],[572,5470,5472],{"className":5471},[639],[572,5473,5475],{"className":5474,"style":675},[643],[572,5476],{},[572,5478],{"className":5479,"style":905},[843],[572,5481,779],{"className":5482},[743],[572,5484],{"className":5485,"style":905},[843],[572,5487,5489,5492,5495],{"className":5488},[613],[572,5490],{"className":5491,"style":858},[617],[572,5493,1693],{"className":5494},[622],[572,5496,1930],{"className":5497},[1650],". Das ist lineare Konvergenz mit ",[572,5500,5502,5521],{"className":5501},[575],[572,5503,5505],{"className":5504},[579],[581,5506,5507],{"xmlns":583},[585,5508,5509,5518],{},[588,5510,5511,5513,5515],{},[594,5512,1013],{},[697,5514,766],{},[1005,5516,5517],{},"0,5",[601,5519,5520],{"encoding":603},"C = 0{,}5",[572,5522,5524,5542],{"className":5523,"ariaHidden":609},[608],[572,5525,5527,5530,5533,5536,5539],{"className":5526},[613],[572,5528],{"className":5529,"style":1312},[617],[572,5531,1013],{"className":5532,"style":1109},[622,626],[572,5534],{"className":5535,"style":844},[843],[572,5537,766],{"className":5538},[848],[572,5540],{"className":5541,"style":844},[843],[572,5543,5545,5548,5551,5557],{"className":5544},[613],[572,5546],{"className":5547,"style":2436},[617],[572,5549,1468],{"className":5550},[622],[572,5552,5554],{"className":5553},[622],[572,5555,2447],{"className":5556},[2446],[572,5558,2245],{"className":5559},[622],": Pro Schritt gewinnt man nur etwa ",[572,5562,5564,5579],{"className":5563},[575],[572,5565,5567],{"className":5566},[579],[581,5568,5569],{"xmlns":583},[585,5570,5571,5576],{},[588,5572,5573],{},[1005,5574,5575],{},"0,3",[601,5577,5578],{"encoding":603},"0{,}3",[572,5580,5582],{"className":5581,"ariaHidden":609},[608],[572,5583,5585,5588,5591,5597],{"className":5584},[613],[572,5586],{"className":5587,"style":2436},[617],[572,5589,1468],{"className":5590},[622],[572,5592,5594],{"className":5593},[622],[572,5595,2447],{"className":5596},[2446],[572,5598,3850],{"className":5599},[622],[559,5601,5603],{"id":5602},"typische-fehler","Typische Fehler",[1171,5605,5606,5765,5768,5771],{},[1174,5607,5608,5609,5659,5660,5710,5711,5764],{},"Bei ",[572,5610,5612,5629],{"className":5611},[575],[572,5613,5615],{"className":5614},[579],[581,5616,5617],{"xmlns":583},[585,5618,5619,5627],{},[588,5620,5621,5623,5625],{},[594,5622,564],{},[697,5624,766],{},[1005,5626,1007],{},[601,5628,1200],{"encoding":603},[572,5630,5632,5650],{"className":5631,"ariaHidden":609},[608],[572,5633,5635,5638,5641,5644,5647],{"className":5634},[613],[572,5636],{"className":5637,"style":976},[617],[572,5639,564],{"className":5640},[622,626],[572,5642],{"className":5643,"style":844},[843],[572,5645,766],{"className":5646},[848],[572,5648],{"className":5649,"style":844},[843],[572,5651,5653,5656],{"className":5652},[613],[572,5654],{"className":5655,"style":1228},[617],[572,5657,1007],{"className":5658},[622]," die Bedingung ",[572,5661,5663,5680],{"className":5662},[575],[572,5664,5666],{"className":5665},[579],[581,5667,5668],{"xmlns":583},[585,5669,5670,5678],{},[588,5671,5672,5674,5676],{},[594,5673,1013],{},[697,5675,1249],{},[1005,5677,1007],{},[601,5679,1254],{"encoding":603},[572,5681,5683,5701],{"className":5682,"ariaHidden":609},[608],[572,5684,5686,5689,5692,5695,5698],{"className":5685},[613],[572,5687],{"className":5688,"style":1264},[617],[572,5690,1013],{"className":5691,"style":1109},[622,626],[572,5693],{"className":5694,"style":844},[843],[572,5696,1249],{"className":5697},[848],[572,5699],{"className":5700,"style":844},[843],[572,5702,5704,5707],{"className":5703},[613],[572,5705],{"className":5706,"style":1228},[617],[572,5708,1007],{"className":5709},[622]," vergessen. Mit ",[572,5712,5714,5733],{"className":5713},[575],[572,5715,5717],{"className":5716},[579],[581,5718,5719],{"xmlns":583},[585,5720,5721,5730],{},[588,5722,5723,5725,5728],{},[594,5724,1013],{},[697,5726,5727],{},"≥",[1005,5729,1007],{},[601,5731,5732],{"encoding":603},"C \\geq 1",[572,5734,5736,5755],{"className":5735,"ariaHidden":609},[608],[572,5737,5739,5743,5746,5749,5752],{"className":5738},[613],[572,5740],{"className":5741,"style":5742},[617],"height:0.8193em;vertical-align:-0.136em;",[572,5744,1013],{"className":5745,"style":1109},[622,626],[572,5747],{"className":5748,"style":844},[843],[572,5750,5727],{"className":5751},[848],[572,5753],{"className":5754,"style":844},[843],[572,5756,5758,5761],{"className":5757},[613],[572,5759],{"className":5760,"style":1228},[617],[572,5762,1007],{"className":5763},[622]," muss der Fehler nicht kleiner werden.",[1174,5766,5767],{},"Die Ordnung aus den ersten, noch weit entfernten Schritten schätzen. Die Schätzung wird erst nahe am Grenzwert verlässlich.",[1174,5769,5770],{},"Quadratische Konvergenz von Newton auch bei mehrfachen Nullstellen erwarten. Dort konvergiert das Verfahren nur linear.",[1174,5772,5773],{},"Ordnung und Aufwand verwechseln: Das Sekantenverfahren hat eine kleinere Ordnung als Newton, braucht aber keine Ableitung und pro Schritt nur eine Funktionsauswertung.",{"title":5775,"searchDepth":5776,"depth":5776,"links":5777},"",2,[5778,5779,5780],{"id":561,"depth":5776,"text":562},{"id":2926,"depth":5776,"text":2927},{"id":5602,"depth":5776,"text":5603},[5782,5785,5788,5791,5794,5797,5800,5803,5806,5809,5812,5815,5818],{"lhs":5783,"rhs":5784},"(1 + 2\u002F1)\u002F2","1.5",{"lhs":5786,"rhs":5787},"(1.5 + 2\u002F1.5)\u002F2","17\u002F12",{"lhs":5789,"rhs":5790},"(17\u002F12 + 2\u002F(17\u002F12))\u002F2","577\u002F408",{"lhs":5792,"rhs":5793},"round(1.5 - sqrt(2), 4)","0.0858",{"lhs":5795,"rhs":5796},"round(17\u002F12 - sqrt(2), 4)","0.0025",{"lhs":5798,"rhs":5799},"round((577\u002F408 - sqrt(2))*1e6, 1)","2.1",{"lhs":5801,"rhs":5802},"round(log((577\u002F408 - sqrt(2))\u002F(17\u002F12 - sqrt(2)))\u002Flog((17\u002F12 - sqrt(2))\u002F(1.5 - sqrt(2))), 2)","1.98",{"lhs":5804,"rhs":5805},"2\u002F(2*2*sqrt(2))","1\u002F(2*sqrt(2))",{"lhs":5807,"rhs":5808},"round(1\u002F(2*sqrt(2)), 2)","0.35",{"lhs":5810,"rhs":5811},"(x\u002F2 + 1) - 2","(x - 2)\u002F2",{"lhs":5813,"rhs":5814},"((1 + sqrt(5))\u002F2)^2","(1 + sqrt(5))\u002F2 + 1",{"lhs":5816,"rhs":5817},"round((1 + sqrt(5))\u002F2, 3)","1.618",{"lhs":5819,"rhs":5820},"round(-log10(0.5), 2)","0.3","p \\geq 1,\\ C > 0,\\ C \u003C 1 \\text{ falls } p = 1,\\ k \\geq k_0","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>p\u003C\u002Fmi>\u003Cmo>≥\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">p \\geq 1,\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:0.8304em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">p\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>\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>C\u003C\u002Fmi>\u003Cmo>>\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">C > 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:0.7224em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0715em;\">C\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\">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>C\u003C\u002Fmi>\u003Cmo><\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">C < 1\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:0.7224em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0715em;\">C\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:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">falls\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>p\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">p = 1,\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:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">p\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>\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>k\u003C\u002Fmi>\u003Cmo>≥\u003C\u002Fmo>\u003Cmsub>\u003Cmi>k\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">k \\geq k_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:0.8304em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\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:0.8444em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0315em;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\">0\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>",null,"md","order-of-convergence","|x_{k+1} - x^*| \\leq C\\,|x_k - x^*|^p","\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>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmrow>\u003Cmi>k\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003C\u002Fmsub>\u003Cmo>−\u003C\u002Fmo>\u003Cmsup>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>∗\u003C\u002Fmo>\u003C\u002Fmsup>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmo>≤\u003C\u002Fmo>\u003Cmi>C\u003C\u002Fmi>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>−\u003C\u002Fmo>\u003Cmsup>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>∗\u003C\u002Fmo>\u003C\u002Fmsup>\u003Cmsup>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmi>p\u003C\u002Fmi>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">|x_{k+1} - x^*| \\leq C\\,|x_k - x^*|^p\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:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">∣\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:0.3361em;\">\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:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"mbin mtight\">+\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">1\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:0.2083em;\">\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:1em;vertical-align:-0.25em;\">\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:0.7387em;\">\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=\"mbin mtight\">∗\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">∣\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:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0715em;\">C\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">∣\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:0.3361em;\">\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\" style=\"margin-right:0.0315em;\">k\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:1em;vertical-align:-0.25em;\">\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:0.7387em;\">\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=\"mbin mtight\">∗\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">∣\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7144em;\">\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 mathnormal mtight\">p\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\u002Fkonvergenzordnung",[],[5834,5835,5836,5837],"newton-method","bisection-method","secant-method","fixed-point-iteration",{"title":548,"description":5775},"de\u002Fformulas\u002Fmath\u002Fnumerics\u002Fkonvergenzordnung","Die Konvergenzordnung p gibt an, wie schnell der Fehler eines Iterationsverfahrens von Schritt zu Schritt schrumpft.",[5842,5843,5844,5845],"konvergenz","iterationsverfahren","fehleranalyse","newton-verfahren",[5847,5850,5853,5855,5858],{"symbol":604,"meaning":5848,"symbolHtml":5849},"Näherung nach k Iterationsschritten","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmsub>\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:0.5806em;vertical-align:-0.15em;\">\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:0.3361em;\">\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\" style=\"margin-right:0.0315em;\">k\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":702,"meaning":5851,"symbolHtml":5852},"gesuchter Grenzwert, z.B. eine Nullstelle","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsup>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>∗\u003C\u002Fmo>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x^*\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:0.6887em;\">\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:0.6887em;\">\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=\"mbin mtight\">∗\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":564,"meaning":548,"symbolHtml":5854},"\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>p\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation 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