数值计算(二分法、简单迭代法、Newton迭代法、弦截法(割线法、双点弦法))2本科生实验报告实验课程数值计算方法学院名称信息科学与技术学院专业名称计算机科学与技术学生姓名学生学号指导教师实验地点实验成绩二〇一六年五月二〇一六年五月3实验一非线性方程求根1.1问题描述实验目的:掌握非线性方程求根的基本步骤及方法,。实验内容:试分别用二分法、简单迭代法、Newton迭代法、弦截法(割线法、双点弦法),求x5-3x3+x-1=0在区间[-8,8]上的全部实根,误差限为10-6。要求:讨论求解的全过程,对所用算法的局部收敛性,优缺点等作分析及比较,第2章算法思想2.1二分法思想:在函数的单调有根区间内,将有根区间不断的二分,寻找方程的解。步骤:1.取中点mid=(x0+x1)/22.若f(mid)=0,则mid为方程的根,否则比较与两端的符号,若与f(x0)异号,则根在[x0,mid]之间,否则在[mid,x1]之间。3并重复上述步骤,直达达到精度要求,则mid为方程的近似解。4开始读入a,b,emid=(a+b)/2F(a)*f(b)<0|a-b|=第3章测试结果及分析测试结果8函数图像函数Y=x5-3x3+x-1二分法(表1-1,1-2,1-3)[-1.6,-1.3]kxkkxkkxk0-1.455-1.5015610-1.504931-1.5256-1.5039111-1.5052-1.48757-1.5050812-1.505043-1.506258-1.5044913-1.505064-1.496889-1.5047914-1.50507表1-1区间[-1.2,-0.9]kxkkxkkxk0-1.055-0.99843710-1.000051-0.9756-1.0007811-0.9999762-1.01257-0.99960912-1.000013-0.993758-1.000213-0.9999944-1.003129-0.99990214-1表1-2区间[1.5,1.8]9kxkkxkkxk01.6571.69102141.6902911.72581.69043151.6902921.687591.69014161.6902931.70625101.69028171.6902841.69687111.69036181.6902851.69219121.6903261.68984131.6903表1-3简单迭代法(表2-1.2-2.2-3)初值-1.5kxkkxkkxk1-1.57-1.5043513-1.504932-1.502178-1.5045314-1.504973-1.502879-1.50466151.504994-1.5034110-1.5047616-1.505015-1.5038111-1.5048317-1.505046-1.5041212-1.5048918-1.50505表2-1初值-1kx1-12-1表2-2初值1.6结果x=1.69028kxkkxkkxk11.681.68862151.6902321.6566991.68927161.690251031.66987101.68967171.6902741.6779111.68991181.6902751.68278121.69006191.6902861.68573131.69015201.6902871.68753141.6902表2-3牛顿迭代法(表3-1.3-2,3-3)初值-1.5结果x=-1.50507kxkkxk1-1.54-1.505042-1.504715-1.505063-1.504976-1.50507表3-1初值-1结果x=-1.50507kx1-12-1表3-2初值1.6结果x=1.69028kxkkxk11.651.6902421.6860261.6902731.6889371.6902841.6898581.69028表3-311双点弦法(表4-1.4-2,4-3)区间[-1.6,-1.3]结果x=-1.50507kxkf(xk)kxkf(xk)1-1.50.031255...