matlab求解超定方程组实例

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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)*

2、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%Bylyqmathfunctionmain()clc;clearall;closeall;%cos(x3)*sin(x2)*sin(x1)-sin(x3)*cos(x1)=-0.9944;%sin(x3)*sin(x2)*sin(x1)+cos(x3)*cos(x1)

3、=-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=[0.30.40.5]            [x,resnorm]=lsqn

4、onlin(@test_fun,x0)F=test_fun(x)functionF=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、(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  0.5000Localminimumfound.Optimizationcompletedbecausethesizeofthegradientislessthant

6、hedefaultvalueofthefunctiontolerance.x=  -0.1028 -0.9390  1.7411resnorm= 5.4490e-009F= 1.0e-004* Columns1through7  0.3522  0.1842 -0.0442  0.1487  0.2260 -0.0936  0.0183 Columns8through9  -0.3600 -0.4160>> 可以发现，误差在1.0e-004级别，还是可以接受的。