solution of a system non linear equations

I have a system of 10 non linear equation. I am tring to solve it by using fsolve.But the problem is that , which gives me one answer. On the other hand Mathematica gives me so many answer among those answer, there is answer I am looking for, which unforunately not given by MATLAB. Perhaps the problem is that tolerance function of fsove is e^{-6}, it may help if I could increase that. Does any one has an idea how to work with it?

[Alex Sha]

Hi, post out your code in details if possible.

[Hassam khan]

function [F]=myfunction(z)

z1=z(1);

z2=z(2);

z3=z(3);

z4=z(4);

z5=z(5);

z6=z(6);

z7=z(7);

z8=z(8);

z9=z(9);

z10=z(10);

%a=[a(1) a(2) a(3) a(4) a(5) a(6) a(7)]

a=[1.897 7.59 2.23 0.056 1 0.0745 0.0196 0 0 0];

F(1)=(z5^2)/(a(4))+(z6^2)/(a(4))-a(5)^2*a(2)-2*a(5)^2*a(1)+(z3^2)/(2*a(1)+a(2))+(z4^2)/(2*a(1)+a(2))-(2*a(5)*z4*a(2))/(2*a(1)+a(2))+(a(5)^2*a(2)^2)/(2*a(1)+a(2))+(z1^2)/(a(1)+a(6))+a(5)^2*z10^2*a(3);

F(2)=(z5*z7)/(a(4))+(z6*z8)/(a(4))+(z2*z3)/(2*a(1)+a(2))+(z1*z3)/(a(1)+a(6));

F(3)=(z5*z9)/(a(4))+(z3*z7)/(2*a(1)+a(2))-(z4*z8)/(2*a(1)+a(2))+(a(5)*z8*a(2))/(2*a(1)+a(2))+(z1*z5)/(a(1)+a(6));

F(4)=-(z6*z7)/(a(4))+(z5*z8)/(a(4))-(z2*z4)/(2*a(1)+a(2))+(a(5)*z2*a(2))/(2*a(1)+a(2))-(z1*z4)/(a(1)+a(6))-(a(5)*z1*a(1))/(a(1)+a(6))+(a(5)*z1*a(6))/(a(1)+a(6));

F(5)=(z7^2)/(a(4))+(z8^2)/(a(4))+(z2^2)/(2*a(1)+a(2))+(z3^2)/(a(1)+a(6))+(z4^2)/(a(1)+a(6))+(2*a(5)*z4*a(1))/(a(1)+a(6))-(2*a(5)*z4*a(6))/(a(1)+a(6))-(4*a(5)^2*a(6)*a(1))/(a(1)+a(6))+(a(5)^2*z10^2*a(1)*a(3))/(a(1)+a(6))+(a(5)^2*z10^2*a(6)*a(3))/(a(1)+a(6));

F(6)=(z7*z9)/(a(4))+(z2*z7)/(2*a(1)+a(2))+(z3*z5)/(a(1)+a(6))+(z4*z6)/(a(1)+a(6))+(a(5)*z6*a(1))/(a(1)+a(6))+(2*z4*a(6))/(a(1)+a(6))-(a(5)*z6*a(6))/(a(1)+a(6))+(4*a(5)*a(1)*a(6))/(a(1)+a(6));

F(7)=-(z6*z9)/(a(4))-(z4*z7)/(2*a(1)+a(2))-(z3*z8)/(2*a(1)+a(2))+(a(5)*z7*a(2))/(2*a(1)+a(2))-(z1*z6)/(a(1)+a(6))-(2*z1*a(6))/(a(1)+a(6));

F(8)=-(z8*z9)/(a(4))-(z2*z8)/(2*a(1)+a(2))+(z4*z5)/(a(1)+a(6))-(z3*z6)/(a(1)+a(6))+(a(5)*z5*a(1))/(a(1)+a(6))-(2*z3*a(6))/(a(1)+a(6))-(a(5)*z5*a(6))/(a(1)+a(6));

F(9)=a(7)*z10^2*a(5)^2+(z9^2)/(a(4))-a(5)^2*a(4)+(z7^2)/(2*a(1)+a(2))+(z8^2)/(2*a(1)+a(2))+(z5^2)/(a(1)+a(6))+(z6^2)/(a(1)+a(6))+(4*z6*a(6))/(a(1)+a(6))-(4*a(1)*a(6))/(a(1)+a(6));

M=[z1 z3+1i*z4 z5+1i*z6;

z3-1i*z4 z2 z7+1i*z8;

z5-1i*z6 z7-1i*z8 z9];

F(10)=det(M);

here is my code.

Answer 1

[Ameer Hamza]

If your system of equations has multiple solutions, fsolve() can only give you a single solution based on the initial point x0. One way is to try different initial points until the desired solution is found, but for a high-dimensional system, this approach can be very inefficient.

The other solution is to use symbolic toolbox and use solve() of vpasolve() functions. These functions are capable of finding multiple solutions to a system of equations.

[Hassam khan]

Thanks Ameer Hamza. .