fslove Equation with variable coefficients

Using fsolve, I want to solve a non linear set of equations such as

k*exp(-exp(-(x(1)+x(2)))) - x(2)*(1+x(1)^2)=0
x(1)*cos(x(2)) + x(2)*sin(x(1)) - 0.5=0

Whereas k is a set of varying coefficients. I want to solve the set of equations using fsolve for each value of k. I used a normal loop with k(i) inside the function and received an error message. Is there a way to perform this with fsolve?

[Torsten]

Please include your code and the exact error message you receive.

Best wishes

Torsten.

Answer 1

[John D'Errico]

Of course you got an error. Solve one problem at a time. Put the loop outside of the call to fsolve.

n = numel(k);
X = zeros(n,2);
x0 = ???
for i = 1:n
  fun = @(x) [k(i)*exp(-exp(-(x(1)+x(2)))) - x(2)*(1+x(1)^2); ...
              x(1)*cos(x(2)) + x(2)*sin(x(1)) - 0.5];

    X(i,:) = fsolve(fun,x0);
  end

At some point, you might decide to learn how to specify a sparse block diagonal jacobian, in which case you could try to solve multiple problems at a time in one call to fsolve. Walk before you run.

[Saeid]

Hi, I tried it and got this error message:

Error in solve_xyvarcoeff (line 8)
    X(i,:) = fsolve(fun,x0);

Caused by:
    Failure in initial objective function evaluation. FSOLVE cannot
    continue.

[Saeid]

I guess I found the mistake: x0 should have had the same dimension as that of the X!