Deconvolution for solving nonlinear system

Dear all,

I have a question on solving nonlinear equations with convolutions. Please help me with codes, ideas or procedures. Here are the equations. Where V,Z11,Z21,Z12,Z22 are known and V is an array of numbers with size(1,100), Z11,Z21,Z12,Z22 are array of complex numbers with same size as V. How can I calculate Vx and Vy? Thank you very very much. Looking forward to your reply.

Best Regards

Zhifei

[Matt J]

What are I1 and I2? Known? Unknown?

[zhifei xu]

I1 and I2 are unknown, you have to substitue them to the first 2 equations.

Answer 1

[Matt J]

Seems like a good candidate for FSOLVE.

[zhifei xu]

But the conv and deconv function does not support symbols

[Matt J]

FSOLVE is not in the Symbolic Math Toolbox. It is a purely numerical solver. It is doubtful (to me) that the equations you've shown have a closed form symbolic solution.

[zhifei xu]

Thanks for your response. The results of my equations will be an array of complex numbers(I guess deconvolved results).I tried to use fsolve to solve a simple deconvolution example.It gives me the error.I do not know why. "fsolve stopped because the problem appears regular as measured by the gradient, but the vector of function values is not near zero as measured by the default value of the function tolerance." And my code is below:

    options=optimset('Algorithm','Levenberg-Marquardt');
    [x,fval] = fsolve(@g,0,options);
    function F=g(x)
        u = [1 0 1 1 ];
        w = [2 7 2 7];
        t=[4 16 9 9]; %the convolution result of u and w
        F =conv(u,x,'same')-t;
    end

[Matt J]

You need to run as follows,

   options=optimset('Algorithm','Levenberg-Marquardt');
    [x,fval] = fsolve(@g,[0,0,0,0],options)
    function F=g(x)
        u = [1 0 1 1 ];
        t=[4 16 9 9]; %the convolution result of u and w
        F =conv(u,x,'same')-t;
    end

[zhifei xu]

Thank you very much, I will try to apply this to solve my equations, i will let you know if i succeed. Thank you so much. Have a nice day!!

[zhifei xu]

@Matt J Hello,

I tried with my equations,however, the results are not reliable. and then I tried with another codes with 2 variables. Matlab said no solutions：No solution found.

fsolve stopped because the last step was ineffective. However, the vector of function values is not near zero, as measured by the default value of the function tolerance.

criteria details here is my code: clc close all a1=zeros(1,4); a2=zeros(1,4); options=optimset('Algorithm','Levenberg-Marquardt'); [x,fval] = fsolve(@g,[a1;a2],options); function F=g(x) u = [1 0 1 1 ]; w = [2 7 2 7]; q=[2 2 1 4]; l=[3 4 4 5]; t=[4 16 9 9]; %the convolution result of u and w tt=[21 37 38 31];%the convolution result of q and l F =[conv(u,x(1),'same')-t;conv(q,x(2),'same')-x(1)-tt]; end