How to solve large linear complex equations

The equations are of the following form:

,

where is known.

“Subsitituting into ,we can obtain 14 linear complex equations. By solving 28 linear equations, we can determine the values for .”

How do I solve the imaginary part and the real part

I plan to use the lsqnonlin function for solving, but there are too many unknowns and defining them with syms becomes cumbersome. Is there a better way to solve this problem?

Answer 1

[Matt J]

Since it is a linear and unconstrained system of equations, just use mldivide, \

[Shengfan Bi]

Thank you very much for your answer, but I am still unsure how to transform this equation into the form AX=B for solving.

[Walter Roberson]

equationsToMatrix

[Shengfan Bi]

Thank you for your response. Here is my code where I separate the imaginary and real parts for computation.

syms phi_delta_real [14 1] real %Declaration
eqns_real=real(sum(conj(phi_delta_real)./(delta_i-2*delta_i).^2))+real(1./delta_i.^2-phi_delta_real);%Objective equation
vars=phi_delta_real;
[A,b] = equationsToMatrix(eqns_real,vars);
x=linsolve(A,b);%Linear solution

[Matt J]

Here is my code where I separate the imaginary and real parts for computation.

I'm not sure you need to do that, but regardless, if your question is now resolved, please Accept-click the Answer.