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",[568,1154,1156,1176],{"className":1155},[571],[568,1157,1159],{"className":1158},[575],[577,1160,1161],{"xmlns":579},[581,1162,1163,1173],{},[584,1164,1165],{},[1166,1167,1168,1170],"msup",{},[587,1169,589],{},[591,1171,1172],{},"∗",[607,1174,1175],{"encoding":609},"x^*",[568,1177,1179],{"className":1178,"ariaHidden":615},[614],[568,1180,1182,1186],{"className":1181},[619],[568,1183],{"className":1184,"style":1185},[623],"height:0.6887em;",[568,1187,1189,1192],{"className":1188},[628],[568,1190,589],{"className":1191},[628,629],[568,1193,1195],{"className":1194},[746],[568,1196,1198],{"className":1197},[750],[568,1199,1201],{"className":1200},[755],[568,1202,1204],{"className":1203,"style":1185},[759],[568,1205,1207,1210],{"style":1206},"top:-3.063em;margin-right:0.05em;",[568,1208],{"className":1209,"style":768},[767],[568,1211,1213],{"className":1212},[772,773,774,775],[568,1214,1172],{"className":1215},[1015,775]," in ",[568,1218,1220,1241],{"className":1219},[571],[568,1221,1223],{"className":1222},[575],[577,1224,1225],{"xmlns":579},[581,1226,1227,1239],{},[584,1228,1229,1231,1233,1235,1237],{},[591,1230,873],{"stretchy":599},[587,1232,876],{},[591,1234,879],{"separator":615},[587,1236,882],{},[591,1238,885],{"stretchy":599},[607,1240,888],{"encoding":609},[568,1242,1244],{"className":1243,"ariaHidden":615},[614],[568,1245,1247,1250,1253,1256,1259,1262,1265],{"className":1246},[619],[568,1248],{"className":1249,"style":648},[623],[568,1251,873],{"className":1252},[655],[568,1254,876],{"className":1255},[628,629],[568,1257,879],{"className":1258},[907],[568,1260],{"className":1261,"style":911},[633],[568,1263,882],{"className":1264},[628,629],[568,1266,885],{"className":1267},[662],".",[1150,1270,1271,1272,1323,1324,1268],{},"Die Iteration konvergiert für jeden Startwert aus ",[568,1273,1275,1296],{"className":1274},[571],[568,1276,1278],{"className":1277},[575],[577,1279,1280],{"xmlns":579},[581,1281,1282,1294],{},[584,1283,1284,1286,1288,1290,1292],{},[591,1285,873],{"stretchy":599},[587,1287,876],{},[591,1289,879],{"separator":615},[587,1291,882],{},[591,1293,885],{"stretchy":599},[607,1295,888],{"encoding":609},[568,1297,1299],{"className":1298,"ariaHidden":615},[614],[568,1300,1302,1305,1308,1311,1314,1317,1320],{"className":1301},[619],[568,1303],{"className":1304,"style":648},[623],[568,1306,873],{"className":1307},[655],[568,1309,876],{"className":1310},[628,629],[568,1312,879],{"className":1313},[907],[568,1315],{"className":1316,"style":911},[633],[568,1318,882],{"className":1319},[628,629],[568,1321,885],{"className":1322},[662]," gegen ",[568,1325,1327,1344],{"className":1326},[571],[568,1328,1330],{"className":1329},[575],[577,1331,1332],{"xmlns":579},[581,1333,1334,1342],{},[584,1335,1336],{},[1166,1337,1338,1340],{},[587,1339,589],{},[591,1341,1172],{},[607,1343,1175],{"encoding":609},[568,1345,1347],{"className":1346,"ariaHidden":615},[614],[568,1348,1350,1353],{"className":1349},[619],[568,1351],{"className":1352,"style":1185},[623],[568,1354,1356,1359],{"className":1355},[628],[568,1357,589],{"className":1358},[628,629],[568,1360,1362],{"className":1361},[746],[568,1363,1365],{"className":1364},[750],[568,1366,1368],{"className":1367},[755],[568,1369,1371],{"className":1370,"style":1185},[759],[568,1372,1373,1376],{"style":1206},[568,1374],{"className":1375,"style":768},[767],[568,1377,1379],{"className":1378},[772,773,774,775],[568,1380,1172],{"className":1381},[1015,775],[1150,1383,1384,1385,1388,1389,1791,1792,1388,1795,1268],{},"Es gilt die ",[665,1386,1387],{},"A-priori-Abschätzung"," ",[568,1390,1392,1460],{"className":1391},[571],[568,1393,1395],{"className":1394},[575],[577,1396,1397],{"xmlns":579},[581,1398,1399,1457],{},[584,1400,1401,1403,1410,1412,1418,1420,1422,1439,1441,1447,1449,1455],{},[587,1402,938],{"mathvariant":937},[716,1404,1405,1407],{},[587,1406,589],{},[587,1408,1409],{},"n",[591,1411,949],{},[1166,1413,1414,1416],{},[587,1415,589],{},[591,1417,1172],{},[587,1419,938],{"mathvariant":937},[591,1421,963],{},[1423,1424,1425,1431],"mfrac",{},[1166,1426,1427,1429],{},[587,1428,966],{},[587,1430,1409],{},[584,1432,1433,1435,1437],{},[721,1434,1109],{},[591,1436,949],{},[587,1438,966],{},[587,1440,938],{"mathvariant":937},[716,1442,1443,1445],{},[587,1444,589],{},[721,1446,1109],{},[591,1448,949],{},[716,1450,1451,1453],{},[587,1452,589],{},[721,1454,723],{},[587,1456,938],{"mathvariant":937},[607,1458,1459],{"encoding":609},"|x_n - x^*| \\leq \\frac{L^n}{1 - L} |x_1 - x_0|",[568,1461,1463,1522,1569,1742],{"className":1462,"ariaHidden":615},[614],[568,1464,1466,1469,1472,1513,1516,1519],{"className":1465},[619],[568,1467],{"className":1468,"style":648},[623],[568,1470,938],{"className":1471},[628],[568,1473,1475,1478],{"className":1474},[628],[568,1476,589],{"className":1477},[628,629],[568,1479,1481],{"className":1480},[746],[568,1482,1484,1505],{"className":1483},[750,751],[568,1485,1487,1502],{"className":1486},[755],[568,1488,1491],{"className":1489,"style":1490},[759],"height:0.1514em;",[568,1492,1493,1496],{"style":763},[568,1494],{"className":1495,"style":768},[767],[568,1497,1499],{"className":1498},[772,773,774,775],[568,1500,1409],{"className":1501},[628,629,775],[568,1503,783],{"className":1504},[782],[568,1506,1508],{"className":1507},[755],[568,1509,1511],{"className":1510,"style":790},[759],[568,1512],{},[568,1514],{"className":1515,"style":1011},[633],[568,1517,949],{"className":1518},[1015],[568,1520],{"className":1521,"style":1011},[633],[568,1523,1525,1528,1557,1560,1563,1566],{"className":1524},[619],[568,1526],{"className":1527,"style":648},[623],[568,1529,1531,1534],{"className":1530},[628],[568,1532,589],{"className":1533},[628,629],[568,1535,1537],{"className":1536},[746],[568,1538,1540],{"className":1539},[750],[568,1541,1543],{"className":1542},[755],[568,1544,1546],{"className":1545,"style":1185},[759],[568,1547,1548,1551],{"style":1206},[568,1549],{"className":1550,"style":768},[767],[568,1552,1554],{"className":1553},[772,773,774,775],[568,1555,1172],{"className":1556},[1015,775],[568,1558,938],{"className":1559},[628],[568,1561],{"className":1562,"style":634},[633],[568,1564,963],{"className":1565},[638],[568,1567],{"className":1568,"style":634},[633],[568,1570,1572,1576,1690,1693,1733,1736,1739],{"className":1571},[619],[568,1573],{"className":1574,"style":1575},[623],"height:1.3143em;vertical-align:-0.4033em;",[568,1577,1579,1583,1687],{"className":1578},[628],[568,1580],{"className":1581},[655,1582],"nulldelimiter",[568,1584,1586],{"className":1585},[1423],[568,1587,1589,1678],{"className":1588},[750,751],[568,1590,1592,1675],{"className":1591},[755],[568,1593,1596,1618,1629],{"className":1594,"style":1595},[759],"height:0.911em;",[568,1597,1599,1603],{"style":1598},"top:-2.655em;",[568,1600],{"className":1601,"style":1602},[767],"height:3em;",[568,1604,1606],{"className":1605},[772,773,774,775],[568,1607,1609,1612,1615],{"className":1608},[628,775],[568,1610,1109],{"className":1611},[628,775],[568,1613,949],{"className":1614},[1015,775],[568,1616,966],{"className":1617},[628,629,775],[568,1619,1621,1624],{"style":1620},"top:-3.23em;",[568,1622],{"className":1623,"style":1602},[767],[568,1625],{"className":1626,"style":1628},[1627],"frac-line","border-bottom-width:0.04em;",[568,1630,1632,1635],{"style":1631},"top:-3.394em;",[568,1633],{"className":1634,"style":1602},[767],[568,1636,1638],{"className":1637},[772,773,774,775],[568,1639,1641],{"className":1640},[628,775],[568,1642,1644,1647],{"className":1643},[628,775],[568,1645,966],{"className":1646},[628,629,775],[568,1648,1650],{"className":1649},[746],[568,1651,1653],{"className":1652},[750],[568,1654,1656],{"className":1655},[755],[568,1657,1660],{"className":1658,"style":1659},[759],"height:0.7385em;",[568,1661,1663,1667],{"style":1662},"top:-2.931em;margin-right:0.0714em;",[568,1664],{"className":1665,"style":1666},[767],"height:2.5em;",[568,1668,1672],{"className":1669},[772,1670,1671,775],"reset-size3","size1",[568,1673,1409],{"className":1674},[628,629,775],[568,1676,783],{"className":1677},[782],[568,1679,1681],{"className":1680},[755],[568,1682,1685],{"className":1683,"style":1684},[759],"height:0.4033em;",[568,1686],{},[568,1688],{"className":1689},[662,1582],[568,1691,938],{"className":1692},[628],[568,1694,1696,1699],{"className":1695},[628],[568,1697,589],{"className":1698},[628,629],[568,1700,1702],{"className":1701},[746],[568,1703,1705,1725],{"className":1704},[750,751],[568,1706,1708,1722],{"className":1707},[755],[568,1709,1711],{"className":1710,"style":760},[759],[568,1712,1713,1716],{"style":763},[568,1714],{"className":1715,"style":768},[767],[568,1717,1719],{"className":1718},[772,773,774,775],[568,1720,1109],{"className":1721},[628,775],[568,1723,783],{"className":1724},[782],[568,1726,1728],{"className":1727},[755],[568,1729,1731],{"className":1730,"style":790},[759],[568,1732],{},[568,1734],{"className":1735,"style":1011},[633],[568,1737,949],{"className":1738},[1015],[568,1740],{"className":1741,"style":1011},[633],[568,1743,1745,1748,1788],{"className":1744},[619],[568,1746],{"className":1747,"style":648},[623],[568,1749,1751,1754],{"className":1750},[628],[568,1752,589],{"className":1753},[628,629],[568,1755,1757],{"className":1756},[746],[568,1758,1760,1780],{"className":1759},[750,751],[568,1761,1763,1777],{"className":1762},[755],[568,1764,1766],{"className":1765,"style":760},[759],[568,1767,1768,1771],{"style":763},[568,1769],{"className":1770,"style":768},[767],[568,1772,1774],{"className":1773},[772,773,774,775],[568,1775,723],{"className":1776},[628,775],[568,1778,783],{"className":1779},[782],[568,1781,1783],{"className":1782},[755],[568,1784,1786],{"className":1785,"style":790},[759],[568,1787],{},[568,1789,938],{"className":1790},[628]," und die ",[665,1793,1794],{},"A-posteriori-Abschätzung",[568,1796,1798,1866],{"className":1797},[571],[568,1799,1801],{"className":1800},[575],[577,1802,1803],{"xmlns":579},[581,1804,1805,1863],{},[584,1806,1807,1809,1815,1817,1823,1825,1827,1839,1841,1847,1849,1861],{},[587,1808,938],{"mathvariant":937},[716,1810,1811,1813],{},[587,1812,589],{},[587,1814,1409],{},[591,1816,949],{},[1166,1818,1819,1821],{},[587,1820,589],{},[591,1822,1172],{},[587,1824,938],{"mathvariant":937},[591,1826,963],{},[1423,1828,1829,1831],{},[587,1830,966],{},[584,1832,1833,1835,1837],{},[721,1834,1109],{},[591,1836,949],{},[587,1838,966],{},[587,1840,938],{"mathvariant":937},[716,1842,1843,1845],{},[587,1844,589],{},[587,1846,1409],{},[591,1848,949],{},[716,1850,1851,1853],{},[587,1852,589],{},[584,1854,1855,1857,1859],{},[587,1856,1409],{},[591,1858,949],{},[721,1860,1109],{},[587,1862,938],{"mathvariant":937},[607,1864,1865],{"encoding":609},"|x_n - x^*| \\leq \\frac{L}{1 - L} |x_n - x_{n-1}|",[568,1867,1869,1927,1974,2108],{"className":1868,"ariaHidden":615},[614],[568,1870,1872,1875,1878,1918,1921,1924],{"className":1871},[619],[568,1873],{"className":1874,"style":648},[623],[568,1876,938],{"className":1877},[628],[568,1879,1881,1884],{"className":1880},[628],[568,1882,589],{"className":1883},[628,629],[568,1885,1887],{"className":1886},[746],[568,1888,1890,1910],{"className":1889},[750,751],[568,1891,1893,1907],{"className":1892},[755],[568,1894,1896],{"className":1895,"style":1490},[759],[568,1897,1898,1901],{"style":763},[568,1899],{"className":1900,"style":768},[767],[568,1902,1904],{"className":1903},[772,773,774,775],[568,1905,1409],{"className":1906},[628,629,775],[568,1908,783],{"className":1909},[782],[568,1911,1913],{"className":1912},[755],[568,1914,1916],{"className":1915,"style":790},[759],[568,1917],{},[568,1919],{"className":1920,"style":1011},[633],[568,1922,949],{"className":1923},[1015],[568,1925],{"className":1926,"style":1011},[633],[568,1928,1930,1933,1962,1965,1968,1971],{"className":1929},[619],[568,1931],{"className":1932,"style":648},[623],[568,1934,1936,1939],{"className":1935},[628],[568,1937,589],{"className":1938},[628,629],[568,1940,1942],{"className":1941},[746],[568,1943,1945],{"className":1944},[750],[568,1946,1948],{"className":1947},[755],[568,1949,1951],{"className":1950,"style":1185},[759],[568,1952,1953,1956],{"style":1206},[568,1954],{"className":1955,"style":768},[767],[568,1957,1959],{"className":1958},[772,773,774,775],[568,1960,1172],{"className":1961},[1015,775],[568,1963,938],{"className":1964},[628],[568,1966],{"className":1967,"style":634},[633],[568,1969,963],{"className":1970},[638],[568,1972],{"className":1973,"style":634},[633],[568,1975,1977,1981,2056,2059,2099,2102,2105],{"className":1976},[619],[568,1978],{"className":1979,"style":1980},[623],"height:1.2757em;vertical-align:-0.4033em;",[568,1982,1984,1987,2053],{"className":1983},[628],[568,1985],{"className":1986},[655,1582],[568,1988,1990],{"className":1989},[1423],[568,1991,1993,2045],{"className":1992},[750,751],[568,1994,1996,2042],{"className":1995},[755],[568,1997,2000,2020,2028],{"className":1998,"style":1999},[759],"height:0.8723em;",[568,2001,2002,2005],{"style":1598},[568,2003],{"className":2004,"style":1602},[767],[568,2006,2008],{"className":2007},[772,773,774,775],[568,2009,2011,2014,2017],{"className":2010},[628,775],[568,2012,1109],{"className":2013},[628,775],[568,2015,949],{"className":2016},[1015,775],[568,2018,966],{"className":2019},[628,629,775],[568,2021,2022,2025],{"style":1620},[568,2023],{"className":2024,"style":1602},[767],[568,2026],{"className":2027,"style":1628},[1627],[568,2029,2030,2033],{"style":1631},[568,2031],{"className":2032,"style":1602},[767],[568,2034,2036],{"className":2035},[772,773,774,775],[568,2037,2039],{"className":2038},[628,775],[568,2040,966],{"className":2041},[628,629,775],[568,2043,783],{"className":2044},[782],[568,2046,2048],{"className":2047},[755],[568,2049,2051],{"className":2050,"style":1684},[759],[568,2052],{},[568,2054],{"className":2055},[662,1582],[568,2057,938],{"className":2058},[628],[568,2060,2062,2065],{"className":2061},[628],[568,2063,589],{"className":2064},[628,629],[568,2066,2068],{"className":2067},[746],[568,2069,2071,2091],{"className":2070},[750,751],[568,2072,2074,2088],{"className":2073},[755],[568,2075,2077],{"className":2076,"style":1490},[759],[568,2078,2079,2082],{"style":763},[568,2080],{"className":2081,"style":768},[767],[568,2083,2085],{"className":2084},[772,773,774,775],[568,2086,1409],{"className":2087},[628,629,775],[568,2089,783],{"className":2090},[782],[568,2092,2094],{"className":2093},[755],[568,2095,2097],{"className":2096,"style":790},[759],[568,2098],{},[568,2100],{"className":2101,"style":1011},[633],[568,2103,949],{"className":2104},[1015],[568,2106],{"className":2107,"style":1011},[633],[568,2109,2111,2114,2164],{"className":2110},[619],[568,2112],{"className":2113,"style":648},[623],[568,2115,2117,2120],{"className":2116},[628],[568,2118,589],{"className":2119},[628,629],[568,2121,2123],{"className":2122},[746],[568,2124,2126,2155],{"className":2125},[750,751],[568,2127,2129,2152],{"className":2128},[755],[568,2130,2132],{"className":2131,"style":760},[759],[568,2133,2134,2137],{"style":763},[568,2135],{"className":2136,"style":768},[767],[568,2138,2140],{"className":2139},[772,773,774,775],[568,2141,2143,2146,2149],{"className":2142},[628,775],[568,2144,1409],{"className":2145},[628,629,775],[568,2147,949],{"className":2148},[1015,775],[568,2150,1109],{"className":2151},[628,775],[568,2153,783],{"className":2154},[782],[568,2156,2158],{"className":2157},[755],[568,2159,2162],{"className":2160,"style":2161},[759],"height:0.2083em;",[568,2163],{},[568,2165,938],{"className":2166},[628],[564,2168,2169,2170,2198,2199,2397,2398,2401,2402,2520,2521,2754,2755,2884],{},"Ist ",[568,2171,2173,2186],{"className":2172},[571],[568,2174,2176],{"className":2175},[575],[577,2177,2178],{"xmlns":579},[581,2179,2180,2184],{},[584,2181,2182],{},[587,2183,596],{},[607,2185,685],{"encoding":609},[568,2187,2189],{"className":2188,"ariaHidden":615},[614],[568,2190,2192,2195],{"className":2191},[619],[568,2193],{"className":2194,"style":695},[623],[568,2196,596],{"className":2197},[628,629]," differenzierbar, kann man ",[568,2200,2202,2258],{"className":2201},[571],[568,2203,2205],{"className":2204},[575],[577,2206,2207],{"xmlns":579},[581,2208,2209,2255],{},[584,2210,2211,2213,2215,2237,2239,2247,2249,2251,2253],{},[587,2212,966],{},[591,2214,593],{},[716,2216,2217,2225],{},[584,2218,2219,2222],{},[587,2220,2221],{},"max",[591,2223,2224],{},"⁡",[584,2226,2227,2229,2231,2233,2235],{},[591,2228,873],{"stretchy":599},[587,2230,876],{},[591,2232,879],{"separator":615},[587,2234,882],{},[591,2236,885],{"stretchy":599},[587,2238,938],{"mathvariant":937},[1166,2240,2241,2243],{},[587,2242,596],{},[591,2244,2246],{"mathvariant":937,"lspace":2245,"rspace":2245},"0em","′",[591,2248,600],{"stretchy":599},[587,2250,589],{},[591,2252,605],{"stretchy":599},[587,2254,938],{"mathvariant":937},[607,2256,2257],{"encoding":609},"L = \\max_{[a, b]} |\\varphi'(x)|",[568,2259,2261,2280],{"className":2260,"ariaHidden":615},[614],[568,2262,2264,2268,2271,2274,2277],{"className":2263},[619],[568,2265],{"className":2266,"style":2267},[623],"height:0.6833em;",[568,2269,966],{"className":2270},[628,629],[568,2272],{"className":2273,"style":634},[633],[568,2275,593],{"className":2276},[638],[568,2278],{"className":2279,"style":634},[633],[568,2281,2283,2287,2346,2349,2352,2385,2388,2391,2394],{"className":2282},[619],[568,2284],{"className":2285,"style":2286},[623],"height:1.1071em;vertical-align:-0.3552em;",[568,2288,2291,2294],{"className":2289},[2290],"mop",[568,2292,2221],{"className":2293},[2290],[568,2295,2297],{"className":2296},[746],[568,2298,2300,2337],{"className":2299},[750,751],[568,2301,2303,2334],{"className":2302},[755],[568,2304,2307],{"className":2305,"style":2306},[759],"height:0.3448em;",[568,2308,2310,2313],{"style":2309},"top:-2.5198em;margin-right:0.05em;",[568,2311],{"className":2312,"style":768},[767],[568,2314,2316],{"className":2315},[772,773,774,775],[568,2317,2319,2322,2325,2328,2331],{"className":2318},[628,775],[568,2320,873],{"className":2321},[655,775],[568,2323,876],{"className":2324},[628,629,775],[568,2326,879],{"className":2327},[907,775],[568,2329,882],{"className":2330},[628,629,775],[568,2332,885],{"className":2333},[662,775],[568,2335,783],{"className":2336},[782],[568,2338,2340],{"className":2339},[755],[568,2341,2344],{"className":2342,"style":2343},[759],"height:0.3552em;",[568,2345],{},[568,2347],{"className":2348,"style":911},[633],[568,2350,938],{"className":2351},[628],[568,2353,2355,2358],{"className":2354},[628],[568,2356,596],{"className":2357},[628,629],[568,2359,2361],{"className":2360},[746],[568,2362,2364],{"className":2363},[750],[568,2365,2367],{"className":2366},[755],[568,2368,2371],{"className":2369,"style":2370},[759],"height:0.7519em;",[568,2372,2373,2376],{"style":1206},[568,2374],{"className":2375,"style":768},[767],[568,2377,2379],{"className":2378},[772,773,774,775],[568,2380,2382],{"className":2381},[628,775],[568,2383,2246],{"className":2384},[628,775],[568,2386,600],{"className":2387},[655],[568,2389,589],{"className":2390},[628,629],[568,2392,605],{"className":2393},[662],[568,2395,938],{"className":2396},[628]," wählen. Die Konvergenz ist im Allgemeinen ",[665,2399,2400],{},"linear",": Der Fehler schrumpft pro Schritt etwa um den Faktor ",[568,2403,2405,2437],{"className":2404},[571],[568,2406,2408],{"className":2407},[575],[577,2409,2410],{"xmlns":579},[581,2411,2412,2434],{},[584,2413,2414,2416,2422,2424,2430,2432],{},[587,2415,938],{"mathvariant":937},[1166,2417,2418,2420],{},[587,2419,596],{},[591,2421,2246],{"mathvariant":937,"lspace":2245,"rspace":2245},[591,2423,600],{"stretchy":599},[1166,2425,2426,2428],{},[587,2427,589],{},[591,2429,1172],{},[591,2431,605],{"stretchy":599},[587,2433,938],{"mathvariant":937},[607,2435,2436],{"encoding":609},"|\\varphi'(x^*)|",[568,2438,2440],{"className":2439,"ariaHidden":615},[614],[568,2441,2443,2447,2450,2482,2485,2514,2517],{"className":2442},[619],[568,2444],{"className":2445,"style":2446},[623],"height:1.0019em;vertical-align:-0.25em;",[568,2448,938],{"className":2449},[628],[568,2451,2453,2456],{"className":2452},[628],[568,2454,596],{"className":2455},[628,629],[568,2457,2459],{"className":2458},[746],[568,2460,2462],{"className":2461},[750],[568,2463,2465],{"className":2464},[755],[568,2466,2468],{"className":2467,"style":2370},[759],[568,2469,2470,2473],{"style":1206},[568,2471],{"className":2472,"style":768},[767],[568,2474,2476],{"className":2475},[772,773,774,775],[568,2477,2479],{"className":2478},[628,775],[568,2480,2246],{"className":2481},[628,775],[568,2483,600],{"className":2484},[655],[568,2486,2488,2491],{"className":2487},[628],[568,2489,589],{"className":2490},[628,629],[568,2492,2494],{"className":2493},[746],[568,2495,2497],{"className":2496},[750],[568,2498,2500],{"className":2499},[755],[568,2501,2503],{"className":2502,"style":1185},[759],[568,2504,2505,2508],{"style":1206},[568,2506],{"className":2507,"style":768},[767],[568,2509,2511],{"className":2510},[772,773,774,775],[568,2512,1172],{"className":2513},[1015,775],[568,2515,605],{"className":2516},[662],[568,2518,938],{"className":2519},[628],". Das Newton-Verfahren ist eine Fixpunktiteration mit ",[568,2522,2524,2577],{"className":2523},[571],[568,2525,2527],{"className":2526},[575],[577,2528,2529],{"xmlns":579},[581,2530,2531,2574],{},[584,2532,2533,2535,2537,2539,2541,2543,2545,2547],{},[587,2534,596],{},[591,2536,600],{"stretchy":599},[587,2538,589],{},[591,2540,605],{"stretchy":599},[591,2542,593],{},[587,2544,589],{},[591,2546,949],{},[1423,2548,2549,2560],{},[584,2550,2551,2554,2556,2558],{},[587,2552,2553],{},"f",[591,2555,600],{"stretchy":599},[587,2557,589],{},[591,2559,605],{"stretchy":599},[584,2561,2562,2568,2570,2572],{},[1166,2563,2564,2566],{},[587,2565,2553],{},[591,2567,2246],{"mathvariant":937,"lspace":2245,"rspace":2245},[591,2569,600],{"stretchy":599},[587,2571,589],{},[591,2573,605],{"stretchy":599},[607,2575,2576],{"encoding":609},"\\varphi(x) = x - \\frac{f(x)}{f'(x)}",[568,2578,2580,2607,2626],{"className":2579,"ariaHidden":615},[614],[568,2581,2583,2586,2589,2592,2595,2598,2601,2604],{"className":2582},[619],[568,2584],{"className":2585,"style":648},[623],[568,2587,596],{"className":2588},[628,629],[568,2590,600],{"className":2591},[655],[568,2593,589],{"className":2594},[628,629],[568,2596,605],{"className":2597},[662],[568,2599],{"className":2600,"style":634},[633],[568,2602,593],{"className":2603},[638],[568,2605],{"className":2606,"style":634},[633],[568,2608,2610,2614,2617,2620,2623],{"className":2609},[619],[568,2611],{"className":2612,"style":2613},[623],"height:0.6667em;vertical-align:-0.0833em;",[568,2615,589],{"className":2616},[628,629],[568,2618],{"className":2619,"style":1011},[633],[568,2621,949],{"className":2622},[1015],[568,2624],{"className":2625,"style":1011},[633],[568,2627,2629,2633],{"className":2628},[619],[568,2630],{"className":2631,"style":2632},[623],"height:1.53em;vertical-align:-0.52em;",[568,2634,2636,2639,2751],{"className":2635},[628],[568,2637],{"className":2638},[655,1582],[568,2640,2642],{"className":2641},[1423],[568,2643,2645,2742],{"className":2644},[750,751],[568,2646,2648,2739],{"className":2647},[755],[568,2649,2652,2707,2715],{"className":2650,"style":2651},[759],"height:1.01em;",[568,2653,2654,2657],{"style":1598},[568,2655],{"className":2656,"style":1602},[767],[568,2658,2660],{"className":2659},[772,773,774,775],[568,2661,2663,2698,2701,2704],{"className":2662},[628,775],[568,2664,2666,2670],{"className":2665},[628,775],[568,2667,2553],{"className":2668,"style":2669},[628,629,775],"margin-right:0.1076em;",[568,2671,2673],{"className":2672},[746],[568,2674,2676],{"className":2675},[750],[568,2677,2679],{"className":2678},[755],[568,2680,2683],{"className":2681,"style":2682},[759],"height:0.6828em;",[568,2684,2686,2689],{"style":2685},"top:-2.786em;margin-right:0.0714em;",[568,2687],{"className":2688,"style":1666},[767],[568,2690,2692],{"className":2691},[772,1670,1671,775],[568,2693,2695],{"className":2694},[628,775],[568,2696,2246],{"className":2697},[628,775],[568,2699,600],{"className":2700},[655,775],[568,2702,589],{"className":2703},[628,629,775],[568,2705,605],{"className":2706},[662,775],[568,2708,2709,2712],{"style":1620},[568,2710],{"className":2711,"style":1602},[767],[568,2713],{"className":2714,"style":1628},[1627],[568,2716,2718,2721],{"style":2717},"top:-3.485em;",[568,2719],{"className":2720,"style":1602},[767],[568,2722,2724],{"className":2723},[772,773,774,775],[568,2725,2727,2730,2733,2736],{"className":2726},[628,775],[568,2728,2553],{"className":2729,"style":2669},[628,629,775],[568,2731,600],{"className":2732},[655,775],[568,2734,589],{"className":2735},[628,629,775],[568,2737,605],{"className":2738},[662,775],[568,2740,783],{"className":2741},[782],[568,2743,2745],{"className":2744},[755],[568,2746,2749],{"className":2747,"style":2748},[759],"height:0.52em;",[568,2750],{},[568,2752],{"className":2753},[662,1582],", bei der für eine einfache Nullstelle ",[568,2756,2758,2790],{"className":2757},[571],[568,2759,2761],{"className":2760},[575],[577,2762,2763],{"xmlns":579},[581,2764,2765,2787],{},[584,2766,2767,2773,2775,2781,2783,2785],{},[1166,2768,2769,2771],{},[587,2770,596],{},[591,2772,2246],{"mathvariant":937,"lspace":2245,"rspace":2245},[591,2774,600],{"stretchy":599},[1166,2776,2777,2779],{},[587,2778,589],{},[591,2780,1172],{},[591,2782,605],{"stretchy":599},[591,2784,593],{},[721,2786,723],{},[607,2788,2789],{"encoding":609},"\\varphi'(x^*) = 0",[568,2791,2793,2875],{"className":2792,"ariaHidden":615},[614],[568,2794,2796,2799,2831,2834,2863,2866,2869,2872],{"className":2795},[619],[568,2797],{"className":2798,"style":2446},[623],[568,2800,2802,2805],{"className":2801},[628],[568,2803,596],{"className":2804},[628,629],[568,2806,2808],{"className":2807},[746],[568,2809,2811],{"className":2810},[750],[568,2812,2814],{"className":2813},[755],[568,2815,2817],{"className":2816,"style":2370},[759],[568,2818,2819,2822],{"style":1206},[568,2820],{"className":2821,"style":768},[767],[568,2823,2825],{"className":2824},[772,773,774,775],[568,2826,2828],{"className":2827},[628,775],[568,2829,2246],{"className":2830},[628,775],[568,2832,600],{"className":2833},[655],[568,2835,2837,2840],{"className":2836},[628],[568,2838,589],{"className":2839},[628,629],[568,2841,2843],{"className":2842},[746],[568,2844,2846],{"className":2845},[750],[568,2847,2849],{"className":2848},[755],[568,2850,2852],{"className":2851,"style":1185},[759],[568,2853,2854,2857],{"style":1206},[568,2855],{"className":2856,"style":768},[767],[568,2858,2860],{"className":2859},[772,773,774,775],[568,2861,1172],{"className":2862},[1015,775],[568,2864,605],{"className":2865},[662],[568,2867],{"className":2868,"style":634},[633],[568,2870,593],{"className":2871},[638],[568,2873],{"className":2874,"style":634},[633],[568,2876,2878,2881],{"className":2877},[619],[568,2879],{"className":2880,"style":1141},[623],[568,2882,723],{"className":2883},[628]," ist.",[559,2886,2888],{"id":2887},"beispiele","Beispiele",[564,2890,2891,2892,1089,2954,3030,3031,3123],{},"Die Gleichung ",[568,2893,2895,2918],{"className":2894},[571],[568,2896,2898],{"className":2897},[575],[577,2899,2900],{"xmlns":579},[581,2901,2902,2915],{},[584,2903,2904,2906,2908,2911,2913],{},[587,2905,589],{},[591,2907,593],{},[587,2909,2910],{},"cos",[591,2912,2224],{},[587,2914,589],{},[607,2916,2917],{"encoding":609},"x = \\cos 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Weil ",[568,3878,3880,3893],{"className":3879},[571],[568,3881,3883],{"className":3882},[575],[577,3884,3885],{"xmlns":579},[581,3886,3887,3891],{},[584,3888,3889],{},[587,3890,966],{},[607,3892,966],{"encoding":609},[568,3894,3896],{"className":3895,"ariaHidden":615},[614],[568,3897,3899,3902],{"className":3898},[619],[568,3900],{"className":3901,"style":2267},[623],[568,3903,966],{"className":3904},[628,629]," nahe bei ",[568,3907,3909,3922],{"className":3908},[571],[568,3910,3912],{"className":3911},[575],[577,3913,3914],{"xmlns":579},[581,3915,3916,3920],{},[584,3917,3918],{},[721,3919,1109],{},[607,3921,1109],{"encoding":609},[568,3923,3925],{"className":3924,"ariaHidden":615},[614],[568,3926,3928,3931],{"className":3927},[619],[568,3929],{"className":3930,"style":1141},[623],[568,3932,1109],{"className":3933},[628]," liegt, konvergiert die Folge langsam und pendelt um den Fixpunkt.",[564,3936,2891,3937,4019,4020,3030,4158,4249,4250,3030,4278,4306,4307,4481,4482,4736,4737,4882,4883,5050,5051,1268],{},[568,3938,3940,3962],{"className":3939},[571],[568,3941,3943],{"className":3942},[575],[577,3944,3945],{"xmlns":579},[581,3946,3947,3959],{},[584,3948,3949,3955,3957],{},[1166,3950,3951,3953],{},[587,3952,589],{},[721,3954,3172],{},[591,3956,593],{},[721,3958,3172],{},[607,3960,3961],{"encoding":609},"x^2 = 2",[568,3963,3965,4010],{"className":3964,"ariaHidden":615},[614],[568,3966,3968,3972,4001,4004,4007],{"className":3967},[619],[568,3969],{"className":3970,"style":3971},[623],"height:0.8141em;",[568,3973,3975,3978],{"className":3974},[628],[568,3976,589],{"className":3977},[628,629],[568,3979,3981],{"className":3980},[746],[568,3982,3984],{"className":3983},[750],[568,3985,3987],{"className":3986},[755],[568,3988,3990],{"className":3989,"style":3971},[759],[568,3991,3992,3995],{"style":1206},[568,3993],{"className":3994,"style":768},[767],[568,3996,3998],{"className":3997},[772,773,774,775],[568,3999,3172],{"className":4000},[628,775],[568,4002],{"className":4003,"style":634},[633],[568,4005,593],{"className":4006},[638],[568,4008],{"className":4009,"style":634},[633],[568,4011,4013,4016],{"className":4012},[619],[568,4014],{"className":4015,"style":1141},[623],[568,4017,3172],{"className":4018},[628]," lässt sich unterschiedlich umformen. Mit ",[568,4021,4023,4051],{"className":4022},[571],[568,4024,4026],{"className":4025},[575],[577,4027,4028],{"xmlns":579},[581,4029,4030,4048],{},[584,4031,4032,4034,4036,4038,4040,4042],{},[587,4033,596],{},[591,4035,600],{"stretchy":599},[587,4037,589],{},[591,4039,605],{"stretchy":599},[591,4041,593],{},[1423,4043,4044,4046],{},[721,4045,3172],{},[587,4047,589],{},[607,4049,4050],{"encoding":609},"\\varphi(x) = 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0",[568,4771,4773,4873],{"className":4772,"ariaHidden":615},[614],[568,4774,4776,4779,4811,4814,4861,4864,4867,4870],{"className":4775},[619],[568,4777],{"className":4778,"style":4354},[623],[568,4780,4782,4785],{"className":4781},[628],[568,4783,596],{"className":4784},[628,629],[568,4786,4788],{"className":4787},[746],[568,4789,4791],{"className":4790},[750],[568,4792,4794],{"className":4793},[755],[568,4795,4797],{"className":4796,"style":2370},[759],[568,4798,4799,4802],{"style":1206},[568,4800],{"className":4801,"style":768},[767],[568,4803,4805],{"className":4804},[772,773,774,775],[568,4806,4808],{"className":4807},[628,775],[568,4809,2246],{"className":4810},[628,775],[568,4812,600],{"className":4813},[655],[568,4815,4817],{"className":4816},[628,4396],[568,4818,4820,4853],{"className":4819},[750,751],[568,4821,4823,4850],{"className":4822},[755],[568,4824,4826,4838],{"className":4825,"style":4406},[759],[568,4827,4829,4832],{"className":4828,"style":4411},[4410],[568,4830],{"className":4831,"style":1602},[767],[568,4833,4835],{"className":4834,"style":4418},[628],[568,4836,3172],{"className":4837},[628],[568,4839,4840,4843],{"style":4424},[568,4841],{"className":4842,"style":1602},[767],[568,4844,4846],{"className":4845,"style":4432},[4431],[4434,4847,4848],{"xmlns":4436,"width":4437,"height":4438,"viewBox":4439,"preserveAspectRatio":4440},[4442,4849],{"d":4444},[568,4851,783],{"className":4852},[782],[568,4854,4856],{"className":4855},[755],[568,4857,4859],{"className":4858,"style":4454},[759],[568,4860],{},[568,4862,605],{"className":4863},[662],[568,4865],{"className":4866,"style":634},[633],[568,4868,593],{"className":4869},[638],[568,4871],{"className":4872,"style":634},[633],[568,4874,4876,4879],{"className":4875},[619],[568,4877],{"className":4878,"style":1141},[623],[568,4880,723],{"className":4881},[628],", und die Folge ",[568,4884,4886,4927],{"className":4885},[571],[568,4887,4889],{"className":4888},[575],[577,4890,4891],{"xmlns":579},[581,4892,4893,4924],{},[584,4894,4895,4897,4900,4903,4906,4908,4910,4918,4920,4922],{},[721,4896,1109],{},[591,4898,4899],{"separator":615},";",[968,4901,4902],{}," ",[721,4904,4905],{},"1,5",[591,4907,4899],{"separator":615},[968,4909,4902],{},[1423,4911,4912,4915],{},[721,4913,4914],{},"17",[721,4916,4917],{},"12",[591,4919,4899],{"separator":615},[968,4921,4902],{},[591,4923,3200],{},[607,4925,4926],{"encoding":609},"1;\\ 1{,}5;\\ \\frac{17}{12};\\ \\ldots",[568,4928,4930],{"className":4929,"ariaHidden":615},[614],[568,4931,4933,4936,4939,4942,4945,4948,4951,4957,4961,4964,4967,4970,5038,5041,5044,5047],{"className":4932},[619],[568,4934],{"className":4935,"style":4087},[623],[568,4937,1109],{"className":4938},[628],[568,4940,4899],{"className":4941},[907],[568,4943,4902],{"className":4944},[633],[568,4946],{"className":4947,"style":911},[633],[568,4949,1109],{"className":4950},[628],[568,4952,4954],{"className":4953},[628],[568,4955,879],{"className":4956},[907],[568,4958,4960],{"className":4959},[628],"5",[568,4962,4899],{"className":4963},[907],[568,4965,4902],{"className":4966},[633],[568,4968],{"className":4969,"style":911},[633],[568,4971,4973,4976,5035],{"className":4972},[628],[568,4974],{"className":4975},[655,1582],[568,4977,4979],{"className":4978},[1423],[568,4980,4982,5027],{"className":4981},[750,751],[568,4983,4985,5024],{"className":4984},[755],[568,4986,4988,5002,5010],{"className":4987,"style":4106},[759],[568,4989,4990,4993],{"style":1598},[568,4991],{"className":4992,"style":1602},[767],[568,4994,4996],{"className":4995},[772,773,774,775],[568,4997,4999],{"className":4998},[628,775],[568,5000,4917],{"className":5001},[628,775],[568,5003,5004,5007],{"style":1620},[568,5005],{"className":5006,"style":1602},[767],[568,5008],{"className":5009,"style":1628},[1627],[568,5011,5012,5015],{"style":1631},[568,5013],{"className":5014,"style":1602},[767],[568,5016,5018],{"className":5017},[772,773,774,775],[568,5019,5021],{"className":5020},[628,775],[568,5022,4914],{"className":5023},[628,775],[568,5025,783],{"className":5026},[782],[568,5028,5030],{"className":5029},[755],[568,5031,5033],{"className":5032,"style":4152},[759],[568,5034],{},[568,5036],{"className":5037},[662,1582],[568,5039,4899],{"className":5040},[907],[568,5042,4902],{"className":5043},[633],[568,5045],{"className":5046,"style":911},[633],[568,5048,3200],{"className":5049},[3489]," konvergiert sehr schnell gegen ",[568,5052,5054,5070],{"className":5053},[571],[568,5055,5057],{"className":5056},[575],[577,5058,5059],{"xmlns":579},[581,5060,5061,5067],{},[584,5062,5063],{},[4330,5064,5065],{},[721,5066,3172],{},[607,5068,5069],{"encoding":609},"\\sqrt{2}",[568,5071,5073],{"className":5072,"ariaHidden":615},[614],[568,5074,5076,5080],{"className":5075},[619],[568,5077],{"className":5078,"style":5079},[623],"height:1.04em;vertical-align:-0.1328em;",[568,5081,5083],{"className":5082},[628,4396],[568,5084,5086,5119],{"className":5085},[750,751],[568,5087,5089,5116],{"className":5088},[755],[568,5090,5092,5104],{"className":5091,"style":4406},[759],[568,5093,5095,5098],{"className":5094,"style":4411},[4410],[568,5096],{"className":5097,"style":1602},[767],[568,5099,5101],{"className":5100,"style":4418},[628],[568,5102,3172],{"className":5103},[628],[568,5105,5106,5109],{"style":4424},[568,5107],{"className":5108,"style":1602},[767],[568,5110,5112],{"className":5111,"style":4432},[4431],[4434,5113,5114],{"xmlns":4436,"width":4437,"height":4438,"viewBox":4439,"preserveAspectRatio":4440},[4442,5115],{"d":4444},[568,5117,783],{"className":5118},[782],[568,5120,5122],{"className":5121},[755],[568,5123,5125],{"className":5124,"style":4454},[759],[568,5126],{},[564,5128,5129,5130,3030,5191,5365,5366,5394,5395,5640,5641,5778,5779,5831,5832,5884],{},"Mit ",[568,5131,5133,5152],{"className":5132},[571],[568,5134,5136],{"className":5135},[575],[577,5137,5138],{"xmlns":579},[581,5139,5140,5149],{},[584,5141,5142,5144,5146],{},[587,5143,966],{},[591,5145,593],{},[721,5147,5148],{},"0,5",[607,5150,5151],{"encoding":609},"L = 0{,}5",[568,5153,5155,5173],{"className":5154,"ariaHidden":615},[614],[568,5156,5158,5161,5164,5167,5170],{"className":5157},[619],[568,5159],{"className":5160,"style":2267},[623],[568,5162,966],{"className":5163},[628,629],[568,5165],{"className":5166,"style":634},[633],[568,5168,593],{"className":5169},[638],[568,5171],{"className":5172,"style":634},[633],[568,5174,5176,5179,5182,5188],{"className":5175},[619],[568,5177],{"className":5178,"style":3308},[623],[568,5180,723],{"className":5181},[628],[568,5183,5185],{"className":5184},[628],[568,5186,879],{"className":5187},[907],[568,5189,4960],{"className":5190},[628],[568,5192,5194,5228],{"className":5193},[571],[568,5195,5197],{"className":5196},[575],[577,5198,5199],{"xmlns":579},[581,5200,5201,5225],{},[584,5202,5203,5205,5211,5213,5219,5221,5223],{},[587,5204,938],{"mathvariant":937},[716,5206,5207,5209],{},[587,5208,589],{},[721,5210,1109],{},[591,5212,949],{},[716,5214,5215,5217],{},[587,5216,589],{},[721,5218,723],{},[587,5220,938],{"mathvariant":937},[591,5222,593],{},[721,5224,5148],{},[607,5226,5227],{"encoding":609},"|x_1 - x_0| = 0{,}5",[568,5229,5231,5289,5347],{"className":5230,"ariaHidden":615},[614],[568,5232,5234,5237,5240,5280,5283,5286],{"className":5233},[619],[568,5235],{"className":5236,"style":648},[623],[568,5238,938],{"className":5239},[628],[568,5241,5243,5246],{"className":5242},[628],[568,5244,589],{"className":5245},[628,629],[568,5247,5249],{"className":5248},[746],[568,5250,5252,5272],{"className":5251},[750,751],[568,5253,5255,5269],{"className":5254},[755],[568,5256,5258],{"className":5257,"style":760},[759],[568,5259,5260,5263],{"style":763},[568,5261],{"className":5262,"style":768},[767],[568,5264,5266],{"className":5265},[772,773,774,775],[568,5267,1109],{"className":5268},[628,775],[568,5270,783],{"className":5271},[782],[568,5273,5275],{"className":5274},[755],[568,5276,5278],{"className":5277,"style":790},[759],[568,5279],{},[568,5281],{"className":5282,"style":1011},[633],[568,5284,949],{"className":5285},[1015],[568,5287],{"className":5288,"style":1011},[633],[568,5290,5292,5295,5335,5338,5341,5344],{"className":5291},[619],[568,5293],{"className":5294,"style":648},[623],[568,5296,5298,5301],{"className":5297},[628],[568,5299,589],{"className":5300},[628,629],[568,5302,5304],{"className":5303},[746],[568,5305,5307,5327],{"className":5306},[750,751],[568,5308,5310,5324],{"className":5309},[755],[568,5311,5313],{"className":5312,"style":760},[759],[568,5314,5315,5318],{"style":763},[568,5316],{"className":5317,"style":768},[767],[568,5319,5321],{"className":5320},[772,773,774,775],[568,5322,723],{"className":5323},[628,775],[568,5325,783],{"className":5326},[782],[568,5328,5330],{"className":5329},[755],[568,5331,5333],{"className":5332,"style":790},[759],[568,5334],{},[568,5336,938],{"className":5337},[628],[568,5339],{"className":5340,"style":634},[633],[568,5342,593],{"className":5343},[638],[568,5345],{"className":5346,"style":634},[633],[568,5348,5350,5353,5356,5362],{"className":5349},[619],[568,5351],{"className":5352,"style":3308},[623],[568,5354,723],{"className":5355},[628],[568,5357,5359],{"className":5358},[628],[568,5360,879],{"className":5361},[907],[568,5363,4960],{"className":5364},[628]," ist der Fehler nach ",[568,5367,5369,5382],{"className":5368},[571],[568,5370,5372],{"className":5371},[575],[577,5373,5374],{"xmlns":579},[581,5375,5376,5380],{},[584,5377,5378],{},[587,5379,1409],{},[607,5381,1409],{"encoding":609},[568,5383,5385],{"className":5384,"ariaHidden":615},[614],[568,5386,5388,5391],{"className":5387},[619],[568,5389],{"className":5390,"style":624},[623],[568,5392,1409],{"className":5393},[628,629]," Schritten höchstens ",[568,5396,5398,5437],{"className":5397},[571],[568,5399,5401],{"className":5400},[575],[577,5402,5403],{"xmlns":579},[581,5404,5405,5434],{},[584,5406,5407,5417,5420,5422,5424],{},[1423,5408,5409,5415],{},[1166,5410,5411,5413],{},[721,5412,5148],{},[587,5414,1409],{},[721,5416,5148],{},[591,5418,5419],{},"⋅",[721,5421,5148],{},[591,5423,593],{},[1166,5425,5426,5428],{},[721,5427,3172],{},[584,5429,5430,5432],{},[591,5431,949],{},[587,5433,1409],{},[607,5435,5436],{"encoding":609},"\\frac{0{,}5^n}{0{,}5} \\cdot 0{,}5 = 2^{-n}",[568,5438,5440,5571,5598],{"className":5439,"ariaHidden":615},[614],[568,5441,5443,5447,5562,5565,5568],{"className":5442},[619],[568,5444],{"className":5445,"style":5446},[623],"height:1.4442em;vertical-align:-0.4811em;",[568,5448,5450,5453,5559],{"className":5449},[628],[568,5451],{"className":5452},[655,1582],[568,5454,5456],{"className":5455},[1423],[568,5457,5459,5550],{"className":5458},[750,751],[568,5460,5462,5547],{"className":5461},[755],[568,5463,5466,5489,5497],{"className":5464,"style":5465},[759],"height:0.9631em;",[568,5467,5468,5471],{"style":1598},[568,5469],{"className":5470,"style":1602},[767],[568,5472,5474],{"className":5473},[772,773,774,775],[568,5475,5477,5480,5486],{"className":5476},[628,775],[568,5478,723],{"className":5479},[628,775],[568,5481,5483],{"className":5482},[628,775],[568,5484,879],{"className":5485},[907,775],[568,5487,4960],{"className":5488},[628,775],[568,5490,5491,5494],{"style":1620},[568,5492],{"className":5493,"style":1602},[767],[568,5495],{"className":5496,"style":1628},[1627],[568,5498,5500,5503],{"style":5499},"top:-3.4461em;",[568,5501],{"className":5502,"style":1602},[767],[568,5504,5506],{"className":5505},[772,773,774,775],[568,5507,5509,5512,5518],{"className":5508},[628,775],[568,5510,723],{"className":5511},[628,775],[568,5513,5515],{"className":5514},[628,775],[568,5516,879],{"className":5517},[907,775],[568,5519,5521,5524],{"className":5520},[628,775],[568,5522,4960],{"className":5523},[628,775],[568,5525,5527],{"className":5526},[746],[568,5528,5530],{"className":5529},[750],[568,5531,5533],{"className":5532},[755],[568,5534,5536],{"className":5535,"style":1659},[759],[568,5537,5538,5541],{"style":1662},[568,5539],{"className":5540,"style":1666},[767],[568,5542,5544],{"className":5543},[772,1670,1671,775],[568,5545,1409],{"className":5546},[628,629,775],[568,5548,783],{"className":5549},[782],[568,5551,5553],{"className":5552},[755],[568,5554,5557],{"className":5555,"style":5556},[759],"height:0.4811em;",[568,5558],{},[568,5560],{"className":5561},[662,1582],[568,5563],{"className":5564,"style":1011},[633],[568,5566,5419],{"className":5567},[1015],[568,5569],{"className":5570,"style":1011},[633],[568,5572,5574,5577,5580,5586,5589,5592,5595],{"className":5573},[619],[568,5575],{"className":5576,"style":3308},[623],[568,5578,723],{"className":5579},[628],[568,5581,5583],{"className":5582},[628],[568,5584,879],{"className":5585},[907],[568,5587,4960],{"className":5588},[628],[568,5590],{"className":5591,"style":634},[633],[568,5593,593],{"className":5594},[638],[568,5596],{"className":5597,"style":634},[633],[568,5599,5601,5605],{"className":5600},[619],[568,5602],{"className":5603,"style":5604},[623],"height:0.7713em;",[568,5606,5608,5611],{"className":5607},[628],[568,5609,3172],{"className":5610},[628],[568,5612,5614],{"className":5613},[746],[568,5615,5617],{"className":5616},[750],[568,5618,5620],{"className":5619},[755],[568,5621,5623],{"className":5622,"style":5604},[759],[568,5624,5625,5628],{"style":1206},[568,5626],{"className":5627,"style":768},[767],[568,5629,5631],{"className":5630},[772,773,774,775],[568,5632,5634,5637],{"className":5633},[628,775],[568,5635,949],{"className":5636},[628,775],[568,5638,1409],{"className":5639},[628,629,775],". Für ",[568,5642,5644,5680],{"className":5643},[571],[568,5645,5647],{"className":5646},[575],[577,5648,5649],{"xmlns":579},[581,5650,5651,5677],{},[584,5652,5653,5663,5665],{},[1166,5654,5655,5657],{},[721,5656,3172],{},[584,5658,5659,5661],{},[591,5660,949],{},[587,5662,1409],{},[591,5664,963],{},[1166,5666,5667,5670],{},[721,5668,5669],{},"10",[584,5671,5672,5674],{},[591,5673,949],{},[721,5675,5676],{},"6",[607,5678,5679],{"encoding":609},"2^{-n} \\leq 10^{-6}",[568,5681,5683,5734],{"className":5682,"ariaHidden":615},[614],[568,5684,5686,5690,5725,5728,5731],{"className":5685},[619],[568,5687],{"className":5688,"style":5689},[623],"height:0.9073em;vertical-align:-0.136em;",[568,5691,5693,5696],{"className":5692},[628],[568,5694,3172],{"className":5695},[628],[568,5697,5699],{"className":5698},[746],[568,5700,5702],{"className":5701},[750],[568,5703,5705],{"className":5704},[755],[568,5706,5708],{"className":5707,"style":5604},[759],[568,5709,5710,5713],{"style":1206},[568,5711],{"className":5712,"style":768},[767],[568,5714,5716],{"className":5715},[772,773,774,775],[568,5717,5719,5722],{"className":5718},[628,775],[568,5720,949],{"className":5721},[628,775],[568,5723,1409],{"className":5724},[628,629,775],[568,5726],{"className":5727,"style":634},[633],[568,5729,963],{"className":5730},[638],[568,5732],{"className":5733,"style":634},[633],[568,5735,5737,5740,5743],{"className":5736},[619],[568,5738],{"className":5739,"style":3971},[623],[568,5741,1109],{"className":5742},[628],[568,5744,5746,5749],{"className":5745},[628],[568,5747,723],{"className":5748},[628],[568,5750,5752],{"className":5751},[746],[568,5753,5755],{"className":5754},[750],[568,5756,5758],{"className":5757},[755],[568,5759,5761],{"className":5760,"style":3971},[759],[568,5762,5763,5766],{"style":1206},[568,5764],{"className":5765,"style":768},[767],[568,5767,5769],{"className":5768},[772,773,774,775],[568,5770,5772,5775],{"className":5771},[628,775],[568,5773,949],{"className":5774},[628,775],[568,5776,5676],{"className":5777},[628,775]," reichen ",[568,5780,5782,5801],{"className":5781},[571],[568,5783,5785],{"className":5784},[575],[577,5786,5787],{"xmlns":579},[581,5788,5789,5798],{},[584,5790,5791,5793,5795],{},[587,5792,1409],{},[591,5794,593],{},[721,5796,5797],{},"20",[607,5799,5800],{"encoding":609},"n = 20",[568,5802,5804,5822],{"className":5803,"ariaHidden":615},[614],[568,5805,5807,5810,5813,5816,5819],{"className":5806},[619],[568,5808],{"className":5809,"style":624},[623],[568,5811,1409],{"className":5812},[628,629],[568,5814],{"className":5815,"style":634},[633],[568,5817,593],{"className":5818},[638],[568,5820],{"className":5821,"style":634},[633],[568,5823,5825,5828],{"className":5824},[619],[568,5826],{"className":5827,"style":1141},[623],[568,5829,5797],{"className":5830},[628]," Schritte, ",[568,5833,5835,5854],{"className":5834},[571],[568,5836,5838],{"className":5837},[575],[577,5839,5840],{"xmlns":579},[581,5841,5842,5851],{},[584,5843,5844,5846,5848],{},[587,5845,1409],{},[591,5847,593],{},[721,5849,5850],{},"19",[607,5852,5853],{"encoding":609},"n = 19",[568,5855,5857,5875],{"className":5856,"ariaHidden":615},[614],[568,5858,5860,5863,5866,5869,5872],{"className":5859},[619],[568,5861],{"className":5862,"style":624},[623],[568,5864,1409],{"className":5865},[628,629],[568,5867],{"className":5868,"style":634},[633],[568,5870,593],{"className":5871},[638],[568,5873],{"className":5874,"style":634},[633],[568,5876,5878,5881],{"className":5877},[619],[568,5879],{"className":5880,"style":1141},[623],[568,5882,5850],{"className":5883},[628]," reicht nach der Schranke noch nicht.",[559,5886,5888],{"id":5887},"typische-fehler","Typische Fehler",[1147,5890,5891,6033,6036],{},[1150,5892,5893,5894,6003,6004,6032],{},"Nur ",[568,5895,5897,5929],{"className":5896},[571],[568,5898,5900],{"className":5899},[575],[577,5901,5902],{"xmlns":579},[581,5903,5904,5926],{},[584,5905,5906,5908,5914,5916,5918,5920,5922,5924],{},[587,5907,938],{"mathvariant":937},[1166,5909,5910,5912],{},[587,5911,596],{},[591,5913,2246],{"mathvariant":937,"lspace":2245,"rspace":2245},[591,5915,600],{"stretchy":599},[587,5917,589],{},[591,5919,605],{"stretchy":599},[587,5921,938],{"mathvariant":937},[591,5923,1106],{},[721,5925,1109],{},[607,5927,5928],{"encoding":609},"|\\varphi'(x)| \u003C 1",[568,5930,5932,5994],{"className":5931,"ariaHidden":615},[614],[568,5933,5935,5938,5941,5973,5976,5979,5982,5985,5988,5991],{"className":5934},[619],[568,5936],{"className":5937,"style":2446},[623],[568,5939,938],{"className":5940},[628],[568,5942,5944,5947],{"className":5943},[628],[568,5945,596],{"className":5946},[628,629],[568,5948,5950],{"className":5949},[746],[568,5951,5953],{"className":5952},[750],[568,5954,5956],{"className":5955},[755],[568,5957,5959],{"className":5958,"style":2370},[759],[568,5960,5961,5964],{"style":1206},[568,5962],{"className":5963,"style":768},[767],[568,5965,5967],{"className":5966},[772,773,774,775],[568,5968,5970],{"className":5969},[628,775],[568,5971,2246],{"className":5972},[628,775],[568,5974,600],{"className":5975},[655],[568,5977,589],{"className":5978},[628,629],[568,5980,605],{"className":5981},[662],[568,5983,938],{"className":5984},[628],[568,5986],{"className":5987,"style":634},[633],[568,5989,1106],{"className":5990},[638],[568,5992],{"className":5993,"style":634},[633],[568,5995,5997,6000],{"className":5996},[619],[568,5998],{"className":5999,"style":1141},[623],[568,6001,1109],{"className":6002},[628]," prüfen und vergessen, dass ",[568,6005,6007,6020],{"className":6006},[571],[568,6008,6010],{"className":6009},[575],[577,6011,6012],{"xmlns":579},[581,6013,6014,6018],{},[584,6015,6016],{},[587,6017,596],{},[607,6019,685],{"encoding":609},[568,6021,6023],{"className":6022,"ariaHidden":615},[614],[568,6024,6026,6029],{"className":6025},[619],[568,6027],{"className":6028,"style":695},[623],[568,6030,596],{"className":6031},[628,629]," das Intervall in sich abbilden muss.",[1150,6034,6035],{},"Eine ungünstige Umformung wählen. Dieselbe Gleichung kann mit einer Iterationsfunktion konvergieren und mit einer anderen divergieren oder pendeln.",[1150,6037,6038,6199,6200,6228,6229,6257,6258,6368],{},[568,6039,6041,6077],{"className":6040},[571],[568,6042,6044],{"className":6043},[575],[577,6045,6046],{"xmlns":579},[581,6047,6048,6074],{},[584,6049,6050,6052,6058,6060,6072],{},[587,6051,938],{"mathvariant":937},[716,6053,6054,6056],{},[587,6055,589],{},[587,6057,1409],{},[591,6059,949],{},[716,6061,6062,6064],{},[587,6063,589],{},[584,6065,6066,6068,6070],{},[587,6067,1409],{},[591,6069,949],{},[721,6071,1109],{},[587,6073,938],{"mathvariant":937},[607,6075,6076],{"encoding":609},"|x_{n} - x_{n-1}|",[568,6078,6080,6141],{"className":6079,"ariaHidden":615},[614],[568,6081,6083,6086,6089,6132,6135,6138],{"className":6082},[619],[568,6084],{"className":6085,"style":648},[623],[568,6087,938],{"className":6088},[628],[568,6090,6092,6095],{"className":6091},[628],[568,6093,589],{"className":6094},[628,629],[568,6096,6098],{"className":6097},[746],[568,6099,6101,6124],{"className":6100},[750,751],[568,6102,6104,6121],{"className":6103},[755],[568,6105,6107],{"className":6106,"style":1490},[759],[568,6108,6109,6112],{"style":763},[568,6110],{"className":6111,"style":768},[767],[568,6113,6115],{"className":6114},[772,773,774,775],[568,6116,6118],{"className":6117},[628,775],[568,6119,1409],{"className":6120},[628,629,775],[568,6122,783],{"className":6123},[782],[568,6125,6127],{"className":6126},[755],[568,6128,6130],{"className":6129,"style":790},[759],[568,6131],{},[568,6133],{"className":6134,"style":1011},[633],[568,6136,949],{"className":6137},[1015],[568,6139],{"className":6140,"style":1011},[633],[568,6142,6144,6147,6196],{"className":6143},[619],[568,6145],{"className":6146,"style":648},[623],[568,6148,6150,6153],{"className":6149},[628],[568,6151,589],{"className":6152},[628,629],[568,6154,6156],{"className":6155},[746],[568,6157,6159,6188],{"className":6158},[750,751],[568,6160,6162,6185],{"className":6161},[755],[568,6163,6165],{"className":6164,"style":760},[759],[568,6166,6167,6170],{"style":763},[568,6168],{"className":6169,"style":768},[767],[568,6171,6173],{"className":6172},[772,773,774,775],[568,6174,6176,6179,6182],{"className":6175},[628,775],[568,6177,1409],{"className":6178},[628,629,775],[568,6180,949],{"className":6181},[1015,775],[568,6183,1109],{"className":6184},[628,775],[568,6186,783],{"className":6187},[782],[568,6189,6191],{"className":6190},[755],[568,6192,6194],{"className":6193,"style":2161},[759],[568,6195],{},[568,6197,938],{"className":6198},[628]," klein für den Fehler halten. Bei ",[568,6201,6203,6216],{"className":6202},[571],[568,6204,6206],{"className":6205},[575],[577,6207,6208],{"xmlns":579},[581,6209,6210,6214],{},[584,6211,6212],{},[587,6213,966],{},[607,6215,966],{"encoding":609},[568,6217,6219],{"className":6218,"ariaHidden":615},[614],[568,6220,6222,6225],{"className":6221},[619],[568,6223],{"className":6224,"style":2267},[623],[568,6226,966],{"className":6227},[628,629]," nahe ",[568,6230,6232,6245],{"className":6231},[571],[568,6233,6235],{"className":6234},[575],[577,6236,6237],{"xmlns":579},[581,6238,6239,6243],{},[584,6240,6241],{},[721,6242,1109],{},[607,6244,1109],{"encoding":609},[568,6246,6248],{"className":6247,"ariaHidden":615},[614],[568,6249,6251,6254],{"className":6250},[619],[568,6252],{"className":6253,"style":1141},[623],[568,6255,1109],{"className":6256},[628]," ist der tatsächliche Fehler bis zu ",[568,6259,6261,6285],{"className":6260},[571],[568,6262,6264],{"className":6263},[575],[577,6265,6266],{"xmlns":579},[581,6267,6268,6282],{},[584,6269,6270],{},[1423,6271,6272,6274],{},[587,6273,966],{},[584,6275,6276,6278,6280],{},[721,6277,1109],{},[591,6279,949],{},[587,6281,966],{},[607,6283,6284],{"encoding":609},"\\frac{L}{1 - L}",[568,6286,6288],{"className":6287,"ariaHidden":615},[614],[568,6289,6291,6294],{"className":6290},[619],[568,6292],{"className":6293,"style":1980},[623],[568,6295,6297,6300,6365],{"className":6296},[628],[568,6298],{"className":6299},[655,1582],[568,6301,6303],{"className":6302},[1423],[568,6304,6306,6357],{"className":6305},[750,751],[568,6307,6309,6354],{"className":6308},[755],[568,6310,6312,6332,6340],{"className":6311,"style":1999},[759],[568,6313,6314,6317],{"style":1598},[568,6315],{"className":6316,"style":1602},[767],[568,6318,6320],{"className":6319},[772,773,774,775],[568,6321,6323,6326,6329],{"className":6322},[628,775],[568,6324,1109],{"className":6325},[628,775],[568,6327,949],{"className":6328},[1015,775],[568,6330,966],{"className":6331},[628,629,775],[568,6333,6334,6337],{"style":1620},[568,6335],{"className":6336,"style":1602},[767],[568,6338],{"className":6339,"style":1628},[1627],[568,6341,6342,6345],{"style":1631},[568,6343],{"className":6344,"style":1602},[767],[568,6346,6348],{"className":6347},[772,773,774,775],[568,6349,6351],{"className":6350},[628,775],[568,6352,966],{"className":6353},[628,629,775],[568,6355,783],{"className":6356},[782],[568,6358,6360],{"className":6359},[755],[568,6361,6363],{"className":6362,"style":1684},[759],[568,6364],{},[568,6366],{"className":6367},[662,1582],"-mal größer.",{"title":6370,"searchDepth":6371,"depth":6371,"links":6372},"",2,[6373,6374,6375],{"id":561,"depth":6371,"text":562},{"id":2887,"depth":6371,"text":2888},{"id":5887,"depth":6371,"text":5888},[6377,6383,6386,6389,6392,6395,6398,6400,6402,6405,6408,6411,6414,6417],{"lhs":6378,"rhs":6379,"where":6380},"L^n\u002F(1 - L)*d0","d0*(L^n + L^(n + 1)\u002F(1 - L))",{"L":6381,"d0":6382},0.5,1.3,{"lhs":6384,"rhs":6385},"round(cos(1), 4)","0.5403",{"lhs":6387,"rhs":6388},"round(cos(cos(1)), 4)","0.8576",{"lhs":6390,"rhs":6391},"round(cos(cos(cos(1))), 4)","0.6543",{"lhs":6393,"rhs":6394},"round(cos(0.7390851332), 6)","0.739085",{"lhs":6396,"rhs":6397},"round(sin(1), 4)","0.8415",{"lhs":6399,"rhs":3172},"2\u002F1",{"lhs":6401,"rhs":1109},"2\u002F2",{"lhs":6403,"rhs":6404},"(1 + 2\u002F1)\u002F2","1.5",{"lhs":6406,"rhs":6407},"(1.5 + 2\u002F1.5)\u002F2","17\u002F12",{"lhs":6409,"rhs":6410},"(sqrt(2) + 2\u002Fsqrt(2))\u002F2","sqrt(2)",{"lhs":6412,"rhs":6413},"0.5^n\u002F(1 - 0.5)*0.5","2^(-n)",{"lhs":6415,"rhs":6416},"round(2^(-20)*10^6, 2)","0.95",{"lhs":6418,"rhs":6419},"round(2^(-19)*10^6, 2)","1.91","\\varphi([a, b]) \\subseteq [a, b],\\ |\\varphi(x) - \\varphi(y)| \\leq L \\, |x - y| \\text{ auf } [a, b],\\ 0 \\leq L \u003C 1,\\ x_0 \\in [a, b]","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>φ\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmo stretchy=\"false\">[\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo stretchy=\"false\">]\u003C\u002Fmo>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>⊆\u003C\u002Fmo>\u003Cmo stretchy=\"false\">[\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo stretchy=\"false\">]\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\varphi([a, b]) \\subseteq [a, 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:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">φ\u003C\u002Fspan>\u003Cspan class=\"mopen\">([\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mclose\">])\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=\"mopen\">[\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mclose\">]\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 mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmi>φ\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>φ\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>y\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmo>≤\u003C\u002Fmo>\u003Cmi>L\u003C\u002Fmi>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>y\u003C\u002Fmi>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">|\\varphi(x) - \\varphi(y)| \\leq L \\, |x - y|\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 mathnormal\">φ\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\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 mathnormal\">φ\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">y\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\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\">L\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">∣\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\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 mathnormal\" style=\"margin-right:0.0359em;\">y\u003C\u002Fspan>\u003Cspan class=\"mord\">∣\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">auf\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmo stretchy=\"false\">[\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo stretchy=\"false\">]\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">[a, 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:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mopen\">[\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mclose\">]\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>\u003Cmn>0\u003C\u002Fmn>\u003Cmo>≤\u003C\u002Fmo>\u003Cmi>L\u003C\u002Fmi>\u003Cmo><\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">0 \\leq L < 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:0.7804em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\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:0.7224em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">L\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>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>∈\u003C\u002Fmo>\u003Cmo stretchy=\"false\">[\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo stretchy=\"false\">]\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x_0 \\in [a, 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:0.6891em;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:0.3011em;\">\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\">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>\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=\"mopen\">[\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mclose\">]\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","fixed-point-iteration","x_{n+1} = \\varphi(x_n), \\qquad |x_n - x^*| \\leq \\frac{L^n}{1 - L} \\, |x_1 - x_0|","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>φ\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"2em\"\u002F>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>−\u003C\u002Fmo>\u003Cmsup>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>∗\u003C\u002Fmo>\u003C\u002Fmsup>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmo>≤\u003C\u002Fmo>\u003Cmfrac>\u003Cmsup>\u003Cmi>L\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsup>\u003Cmrow>\u003Cmn>1\u003C\u002Fmn>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>L\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>−\u003C\u002Fmo>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x_{n+1} = \\varphi(x_n), \\qquad |x_n - x^*| \\leq \\frac{L^n}{1 - L} \\, |x_1 - x_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:0.6389em;vertical-align:-0.2083em;\">\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:0.3011em;\">\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\">n\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:0.2778em;\">\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\">φ\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\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:0.1514em;\">\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\">n\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=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:2em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">∣\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:0.1514em;\">\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\">n\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\">∣\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:2.1297em;vertical-align:-0.7693em;\">\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:1.3603em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">1\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>\u003Cspan class=\"mord mathnormal\">L\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\">\u003Cspan class=\"mord mathnormal\">L\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6644em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7693em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\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:0.3011em;\">\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\">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:0.15em;\">\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 vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\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\">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>\u003Cspan class=\"mord\">∣\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fnumerics\u002Ffixpunktiteration",[],[6433,6434,6435],"newton-method","bisection-method","geometric-series",{"title":548,"description":6370},"de\u002Fformulas\u002Fmath\u002Fnumerics\u002Ffixpunktiteration","Bei der Fixpunktiteration setzt man jede Näherung wieder in φ ein; ist φ eine Kontraktion, konvergiert das gegen den Fixpunkt.",[6440,6441,6442,6443,6444],"fixpunkt","iteration","kontraktion","banachscher fixpunktsatz","näherungsverfahren",[6446,6449,6453,6456,6459,6462],{"symbol":685,"meaning":6447,"symbolHtml":6448},"Iterationsfunktion, deren Fixpunkt gesucht ist","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>φ\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\varphi\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\">φ\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":6450,"meaning":6451,"symbolHtml":6452},"x_n","n-te Näherung","\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>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x_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:0.5806em;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:0.1514em;\">\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\">n\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":726,"meaning":6454,"symbolHtml":6455},"Startwert","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x_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:0.5806em;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:0.3011em;\">\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\">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>",{"symbol":1175,"meaning":6457,"symbolHtml":6458},"Fixpunkt, also Lösung von x = φ(x)","\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":966,"meaning":6460,"symbolHtml":6461},"Kontraktionskonstante (Lipschitz-Konstante kleiner als 1)","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>L\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">L\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\">L\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":1409,"meaning":6463,"symbolHtml":6464},"Anzahl der Iterationsschritte","\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>","I6Tbt-2W5XliQjZUoSt9XP1iTd1-ZmxtKv7mKVJiTz8",[6467,6470,6473],{"stem":6468,"title":6469,"category":391},"de\u002Fformulas\u002Fmath\u002Fnumerics\u002Fbisektionsverfahren","Bisektionsverfahren",{"stem":6471,"title":6472,"category":391},"de\u002Fformulas\u002Fmath\u002Fnumerics\u002Fnewton-verfahren","Newton-Verfahren",{"stem":6474,"title":6475,"category":412},"de\u002Fformulas\u002Fmath\u002Fsequences-series\u002Funendliche-geometrische-reihe","Unendliche geometrische Reihe",1793824265419]