Matlab求解超定方程组实例.doc

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)=-0.8085;cos(x2)*cos(x1)=0.5875;os(x3)*cos(x2)=-0.1001;sin(x3)*cos(x2)=0.5821;-sin(x2)=0.8070; 代码 function 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(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)*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) = sin(x3)*cos(x2)-0.5821; F(9) = -sin(x2)-0.8070; 结果 x0 = ? ? 0.3000 ? ?0.4000 ? ?0.5000 Local minimum found. Optimization completed because the size of the gradient is less than the default value of the function tolerance. stopping criteria details x = ? ?-0.1028 ? -0.9390 ? ?1.7411 resnorm = ? 5.4490e-009 F = ? 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。