MATLAB: Issue with fsolve tolerance

fsolveMATLABOptimization Toolboxtolerances

I am using fsolve to solve an overdetermined system of equations using the levenberg marquadt algorithm.

It works fine although giving the message "Equation solved, fsolve stalled." This is fine for 90% of my cases.

However, for particular systems of equations, my function value that is returned (fval) after saying that the equation is solved (with fsolve stalled) is

0.009486931983140

-0.035516210533842

-0.019252250306780

which is unacceptable for my need.

Since the default function tolerance is 1e-6, why does it accept this as a solution?

Best Answer

Turns out function tolerance is compared with norm(fval)^2and the default tolerance was 1e-3. Simply changed it to 1e-10 (in accordance with my need) and its working well.

Related Solutions

MATLAB: Large scale nonlinear system of equations with sparse Jacobian: cannot find the solution

The answer is "maybe." This is not a huge relative discrepancy. Maybe you should try central finite differences first to see if that makes the discrepancy go down.

DerivativeCheck only applies near the initial point, usually called x0, as explained here. This link also explaines how to set central finite differences.

Alan Weiss

MATLAB mathematical toolbox documentation

MATLAB: Define a stopper in f-solve loop

while true
  [x, fval, exitflag] = fsolve(....);
  if exitflag ~= 1
    break;
  end
end

any of the exit statuses other than +1 could be interpreted as inaccuracy. That can include that the search was going well but that it was taking more iterations than you configured to allow, and can include that the search noticed that round-off error is interfering with pinning down the solution to within the tolerance you requested. Generally speaking, negative exit statuses are the "hard" exits indicating that there is no solution to be found in the area, and positive exits other than +1 indicate that you are running into difficulty with numeric accuracy but that there is likely a solution "nearby".

Best Answer

Related Solutions

MATLAB: Large scale nonlinear system of equations with sparse Jacobian: cannot find the solution

MATLAB: Define a stopper in f-solve loop

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