《非线性方程迭代》PPT课件

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1、§1方程求根与二分法第7章解非线性方程的迭代法一、引言非线性方程的分两类：则可用搜索法求有根区间.x−1012f(x)的符号−−++求根问题的三个方面：存在性，分布，精确化。二、二分法二分法简述.kakbkxkf(xk)符号01234561.01.251.31251.32031.51.3751.34381.32811.251.3751.31251.34381.32811.32031.3242−+−++−−二分法优、缺点；用途。§2迭代法一、不动点迭代kxk012345671.51.357211.330861.325881.324941.324761.324731.32472二

2、、不动点的存在性与迭代法的收敛性三、局部收敛性与收敛阶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׃作业:P290,2,4.§3迭代收敛的加速方法一、埃特金加速收敛方法二、斯蒂芬森迭代法kxkykzk0123451.51.416291.355651.329851.324801.324722.375001.840921.491401.347101.3251812.39655.238882.317281.444351.32714说

3、明:(2.2)不收敛,(3.3)可能收敛;(2.2)线性收敛,(3.3)平方收敛!kxkykzk0123.53.734443.733073.604143.733813.662023.73347§4牛顿法一、牛顿法及其收敛性二、牛顿法应用举例kxk01230.50.571020.567160.56714kxk012341010.75000010.72383710.72380510.723805三、简化牛顿法与牛顿下山法kxkxkxkf(xk)012341.51.347831.325201.324720.617.9发散0.6-1.3841.140625-0.6566431.361

4、810.18661.326280.006671.324720.0000086四、重根情形kxk(1)(2)(3)0123x0x1x2x31.51.4583333331.4366071431.4254976191.51.4166666671.4142156861.4142135621.51.4117647061.4142114381.414213562作业:P291,12,15.§5弦截法kxk012340.50.60.565320.567090.56714§6解非线性方程组的迭代法kx(k)0123(1.5,1.0)T(1.5,0.75)T(1.488095,0.755952

5、)T(1.488034,0.755983)T作业:P290,7,16.