二分法、简单迭代法的matlab代码实现

1、实验一非线性方程的数值解法(一)信息与计算科学金融 崔振威202102034031一、实验目的：熟悉二分法和简单迭代法的算法实现.二、实验内容：教材 P40 2.1.5三、实验要求1根据实验内容编写二分法和简单迭代法的算法实现2简单比拟分析两种算法的误差3试构造不同的迭代格式,分析比拟其收敛性(一)、二分法程序：function ef=bisect(fx,xa,xb,n,delta)% fx是由方程转化的关于 x的函数,有 仅=0.% xa解区间上限% xb解区间下限% n最多循环步数,预防死循环.%delta为允许误差x=xa;fa=eval(fx);x=xb;fb=eval(fx);dis

2、p(' nxaxbxcfc ');for i=1:nxc=(xa+xb)/2;x=xc;fc=eval(fx);X=i,xa,xb,xc,fc;disp(X),if fc*fa<0xb=xc;else xa=xc;endif (xb-xa)<delta,break,endend(二)、简单迭代法程序：function x0,k=iterate (f,x0,eps,N)if nargin<4N=500;endif nargin<3ep=1e-12;endx=x0;x0=x+2*eps;k=0;while abs(x-x0)>eps & k&l

3、t;N x0=x;x=feval(f,x0);k=k+1;endx0=x;if k=N end 解：a、 g(x)=x5-3x3-2x2+2二分法求方程：(1)、 在matlab的命令窗口中输入命令：>> fplot('xA5-3*xA3-2*xA2+2',-3,3);grid得下列图：由上图可得知：方程在-3,3区间有根.(2)、二分法输出结果>> f='xA5-3*xA3-2*xA2+2' f =xA5-3*xA3-2*xA2+2>> bisect(f,-3,3,20,10A(-12)2.0000-3.00000-1.50

4、000.03133.0000-3.0000-1.5000-2.2500-31.61824.0000-2.2500-1.5000-1.8750-8.43015.0000-1.8750-1.5000-1.6875-2.96326.0000-1.6875-1.5000-1.5938-1.21817.0000-1.5938-1.5000-1.5469-0.53828.0000-1.5469-1.5000-1.5234-0.24059.0000-1.5234-1.5000-1.5117-0.101510.0000-1.5117-1.5000-1.5059-0.034311.0000-1.5059-1.5

5、000-1.5029-0.001412.0000-1.5029-1.5000-1.50150.015013.0000-1.5029-1.5015-1.50220.006814.0000-1.5029-1.5022-1.50260.002715.0000-1.5029-1.5026-1.50270.000716.0000-1.5029-1.5027-1.5028-0.000317.0000-1.5028-1.5027-1.50280.000218.0000-1.5028-1.5028-1.5028-0.000119.0000-1.5028-1.5028-1.50280.000120.0000-1

6、.5028-1.5028-1.5028-0.00002、迭代法求方程：迭代法输出结果：>> f=inline('xA5-3*xA3-2*xA2+2');>> x0,k=iterate(fun1,2)x0 =2k =1>> x0,k=iterate(fun1,1.5)x0 =NaNk =6>> x0,k=iterate(fun1,2.5)x0 =NaNk =5(3)、误差分析：由二分法和迭代法输出结果可知,通过定点迭代法得出方程的解误差比二分法大,而利用二分法求出的结果中,可以清楚看出方程等于零时的解,其误差比迭代法小.b、g(x)

7、=cos(sin(x)二分法求方程：(1)、 在matlab的命令窗口中输入命令:>> fplot('cos(sin(x)',-4,4);grid得下列图：由上图可得知：方程在-4,4区间无根.(2)、二分法输出结果>>f='cos(sin(x)' f =cos(sin(x)>> bisect(f,-4,4,20,10A(-12)2.000004.00002.00000.61433.00002.00004.00003.00000.99014.00003.00004.00003.50000.93915.00003.50004.0

8、0003.75000.84116.00003.75004.00003.87500.78427.00003.87504.00003.93750.75548.00003.93754.00003.96880.74129.00003.96884.00003.98440.734110.00003.98444.00003.99220.730511.00003.99224.00003.99610.728812.00003.99614.00003.99800.727913.00003.99804.00003.99900.727514.00003.99904.00003.99950.727315.00003.9

9、9954.00003.99980.727116.00003.99984.00003.99990.727117.00003.99994.00003.99990.727118.00003.99994.00004.00000.727019.00004.00004.00004.00000.727020.00004.00004.00004.00000.72702、迭代法求方程：迭代法输出结果：>> f=inline('cos(sin(x)');>> x0,k=iterate(f,0.5)x0 =0.7682k =15>> x0,k=iterate(f,

10、1)x0 =0.7682k =15>> x0,k=iterate(f,1.5)x0 =0.7682k =16>> x0,k=iterate(f,2)x0 =0.7682k =15>> x0,k=iterate(f,2.5)x0 =0.7682k =14(3)、由于该方程无解,所以无法比拟误差.c、g(x)=x2-sin(x+0.15)二分法求方程：(1)、 在matlab的命令窗口中输入命令:>> fplot('xA2-sin(x+0.15)',-10,10);grid得下列图：-10 -B *64-20246810由上图可得知：

11、方程在-3,3区间有根.(2)、二分法输出结果>> f='xA2-sin(x+0.15)' f =xA2-sin(x+0.15)>> bisect(f,-3,3,30,10A(-12)1.0000-3.00003.00000-0.14942.0000-3.00000-1.50003.22573.0000-1.50000-0.75001.12714.0000-0.75000-0.37500.36375.0000-0.37500-0.18750.07266.0000-0.18750-0.0938-0.04747.0000-0.1875-0.0938-0.14

12、060.01048.0000-0.1406-0.0938-0.1172-0.01919.0000-0.1406-0.1172-0.1289-0.004510.0000-0.1406-0.1289-0.13480.002911.0000-0.1348-0.1289-0.1318-0.000812.0000-0.1348-0.1318-0.13330.001113.0000-0.1333-0.1318-0.13260.000114.0000-0.1326-0.1318-0.1322-0.000315.0000-0.1326-0.1322-0.1324-0.000116.0000-0.1326-0.

13、1324-0.13250.000017.0000-0.1325-0.1324-0.1324-0.000018.0000-0.1325-0.1324-0.1325-0.000019.0000-0.1325-0.1325-0.13250.000020.0000-0.1325-0.1325-0.13250.000021.0000-0.1325-0.1325-0.13250.000022.0000-0.1325-0.1325-0.13250.000023.0000-0.1325-0.1325-0.1325-0.000024.0000-0.1325-0.1325-0.13250.000025.0000-

14、0.1325-0.1325-0.1325-0.000026.0000-0.1325-0.1325-0.13250.000027.0000-0.1325-0.1325-0.13250.000028.0000-0.1325-0.1325-0.13250.000029.0000-0.1325-0.1325-0.13250.000030.0000-0.1325-0.1325-0.1325-0.00002、迭代法求方程：迭代法输出结果：>> f=inline('xA2-sin(x+0.15),);>> x0,k=iterate(f,1.96)x0 =NaNk =12>

15、;> x0,k=iterate(f,0,2)x0 =-0.1494k =1>> x0,k=iterate(f,0.2)x0 =0.3234k =500>> x0,k=iterate(f,0.3)x0 =0.3234k =500>> x0,k=iterate(f,0.001)x0 =0.3234k =500(3)、误差分析：由二分法和迭代法输出结果可知,利用二分法求出的结果中,可以清楚 看出方程等于零时的解,其误差比迭代法小.x-cos(x)d、g(x)=x ''二分法求方程：(1)、 在matlab的命令窗口中输入命令：>>

16、 fplot('xA(x-cos(x)',-1,1);grid得下列图：1210864202x10LLLLLLLL-08-06-04-02()02040608由上图可得知：方程在-1,1区间有根.(2)、二分法输出结果>> f='xA(x-COS(x)'f =xA(x-COS(x)>> bisect(f,-0.1,0.1,20,10A(-12)1.0000-0.10000.1000Inf2.0000-0.10000-0.0500-22.8740 + 3.5309i3.0000-0.05000-0.0250-43.6821 + 3.3947

17、i4.0000-0.02500-0.0125-84.4110 + 3.2958i1.0e+002 *0.0500-0.00010-0.0001-1.6511 + 0.0323i1.0e+002 *0.0600-0.00010-0.0000-3.2580 + 0.0319i1.0e+002 *0.0700-0.00000-0.0000-6.4648 + 0.0317i1.0e+003 *0.0080-0.00000-0.0000-1.2872 + 0.0032i1.0e+003 *0.0090-0.00000-0.0000-2.5679 + 0.0032i1.0e+003 *0.0100-0.0

18、0000-0.0000-5.1285 + 0.0031i1.0e+004 *0.0011-0.00000-0.0000-1.0249 + 0.0003i1.0e+004 *0.0012-0.00000-0.0000-2.0490 + 0.0003i1.0e+004 *0.0013-0.00000-0.0000-4.0971 + 0.0003i1.0e+004 *0.0014-0.00000-0.0000-8.1931 + 0.0003i1.0e+005 *0.0001-0.00000-0.0000-1.6385 + 0.0000i1.0e+005 *0.0002-0.00000-0.0000-3.2769 + 0.0000i1.0e+005 *-0.00000.0002-0.00000-6.5537 + 0.0000i1.0e+006 *-0.00000.0000-0.00000-1.3107 + 0.0000i1.0e+006 *-0.00000.0000-0.00000-2.6215 + 0.0000i1.0e+006 *-0.00000.0000-