I need to use GMRES solver in MATLAB, and I need to play around with the codes parameters and I had a very simple question about its usage.

The documentation of the solver here mentions a parameter tol which they do not seem to have defined except that the defuault value is $10^{-6}$.

What is this number? There don't seem to be any definitions of this anywhere on the web.

Is it the upper-bound on $\frac{||b-Ax_k||}{||b||}$ where we are solving $Ax=b$ and $x_k$ is the current GMRES iterate?


1 Answer 1


It is indeed a tolerance on the relative residual $$ ||b-Ax_k|| / ||b||$$

In the webpage that you mention, you can find this information (very implicitly)

[x,flag,relres] = gmres(A,b,...) also returns the relative residual norm(b-A*x)/norm(b). If flag is 0, relres <= tol. The third output, relres, is the relative residual of the preconditioned system.

Hope it helps!


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