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1、Matlab求解超定方程组实例对于超定方程组，特别是非线性方程组，可以用Matlab基于最小二乘算法来进行求解，例如，求解下列方程组：一个三个未知数，九个方程的非线性方程组：cos(x3)*sin(x2)*sin(x1)-sin(x3)*cos(x1)=-0.9944 ;sin(x3)*sin(x2)*sin(x1)+cos(x3)*cos(x1)=-0.0870;cos(x2)*sin(x1)=-0.0606;cos(x3)*sin(x2)*cos(x1)+sin(x3)*sin(x1)=0.0349;sin(x3)*sin(x2)*cos(x1)-cos(x3)*sin(x1)=-0.80
2、85;cos(x2)*cos(x1)=0.5875;os(x3)*cos(x2)=-0.1001;sin(x3)*cos(x2)=0.5821;-sin(x2)=0.8070;代码% By lyqmathfunction main()clc; clear all; close all;% cos(x3)*sin(x2)*sin(x1)-sin(x3)*cos(x1)=-0.9944 ;% sin(x3)*sin(x2)*sin(x1)+cos(x3)*cos(x1)=-0.0870;% cos(x2)*sin(x1)=-0.0606;% cos(x3)*sin(x2)*cos(x1)+sin(
3、x3)*sin(x1)=0.0349;% sin(x3)*sin(x2)*cos(x1)-cos(x3)*sin(x1)=-0.8085;% cos(x2)*cos(x1)=0.5875;% os(x3)*cos(x2)=-0.1001;% sin(x3)*cos(x2)=0.5821;% -sin(x2)=0.8070;x0 = 0.3 0.4 0.5 x, resnorm = lsqnonlin(test_fun, x0)F = test_fun(x)function F = test_fun(x)x1 = x(1); x2 = x(2); x3 = x(3);F(1) = cos(x3)
4、*sin(x2)*sin(x1)-sin(x3)*cos(x1)+0.9944 ;F(2) = sin(x3)*sin(x2)*sin(x1)+cos(x3)*cos(x1)+0.0870;F(3) = cos(x2)*sin(x1)+0.0606;F(4) = cos(x3)*sin(x2)*cos(x1)+sin(x3)*sin(x1)-0.0349;F(5) = sin(x3)*sin(x2)*cos(x1)-cos(x3)*sin(x1)+0.8085;F(6) = cos(x2)*cos(x1)-0.5875;F(7) = cos(x3)*cos(x2)+0.1001;F(8) =
5、sin(x3)*cos(x2)-0.5821;F(9) = -sin(x2)-0.8070;结果x0 = 0.3000 0.4000 0.5000Local minimum found.Optimization completed because the size of the gradient is less thanthe default value of the function tolerance.x = -0.1028 -0.9390 1.7411resnorm = 5.4490e-009F = 1.0e-004 * Columns 1 through 7 0.3522 0.1842 -0.0442 0.1487 0.2260 -0.0936 0.0183 Columns 8 through 9 -0.3600 -0.4160可以发现，误差在1.0e-004级别，还是可以接受的。
