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1、§1方程求根與二分法第7章非線(xiàn)性方程與方程組的數(shù)值解法一、引言非線(xiàn)性方程的分兩類(lèi)：則可用搜索法求有根區(qū)間.x?1012f(x)的符號(hào)??++求根問(wèn)題的三個(gè)方面：存在性，分布，精確化。二、二分法二分法簡(jiǎn)述.kakbkxkf(xk)符號(hào)01234561.01.251.251.31251.31251.31251.32031.51.51.3751.3751.34381.32811.32811.251.3751.31251.34381.32811.32031.3242?+?++??二分法優(yōu)、缺點(diǎn)?！?不動(dòng)點(diǎn)迭
2、代法及其收斂性一、不動(dòng)點(diǎn)迭代kxk012345671.51.357211.330861.325881.324941.324761.324731.32472二、不動(dòng)點(diǎn)的存在性與迭代法的收斂性三、局部收斂性與收斂階kxk迭代法(1)迭代法(2)迭代法(3)迭代法(4)0123?x0x1x2x3?23987?21.521.5?21.751.734751.732631?21.751.7321431.732051?§3迭代收斂的加速方法一、埃特金加速收斂方法二、斯蒂芬森迭代法kxkykzk0123451.51
3、.416291.355651.329851.324801.324722.375001.840921.491401.347101.3251812.39655.238882.317281.444351.32714說(shuō)明:(2.2)不收斂,(3.3)可能收斂;(2.2)線(xiàn)性收斂,(3.3)平方收斂!kxkykzk0123.53.734443.733073.604143.733813.662023.73347§4牛頓迭代法一、牛頓迭代法及其收斂性二、牛頓法應(yīng)用舉例kxk01230.50.571020.5671
4、60.56714kxk012341010.75000010.72383710.72380510.723805三、簡(jiǎn)化牛頓法與牛頓下山法kxkxkxkf(xk)012341.51.347831.325201.324720.617.9發(fā)散0.6-1.3841.140625-0.6566431.361810.18661.326280.006671.324720.0000086四、重根情形kxk(1)(2)(3)0123x0x1x2x31.51.4583333331.4366071431.425497619
5、1.51.4166666671.4142156861.4142135621.51.4117647061.4142114381.414213562§5弦截法幾何意義：弦截法kxk012340.50.60.565320.567090.56714§7解非線(xiàn)性方程組的迭代法kx(k)0123(1.5,1.0)T(1.5,0.75)T(1.488095,0.755952)T(1.488034,0.755983)T
