Re: tol, atol and rtol behavior of scipy.sparse.linalg solvers

On Mon, May 1, 2023 at 5:21 PM Stefan van der Walt <[email protected]>
wrote:

> On Mon, May 1, 2023, at 11:49, Ilhan Polat wrote:
>
> If atol is actually set to something, then we return max(atol,
> tol*norm(b)). Why max is used I don't understand.
>
> Typically, atol, rtol pair is used as tol = atol + rtol*<some metric>.
> This is more or less what everybody expects from this pair and their naming
> is chosen to reflect this. But I'm a bit lost in all the issues I could
> read.
>
>
> The first formulation — max(atol, rtol*norm(b)) — is what I'd expect.
> I.e., you use atol when answers are small, or rtol for larger answers.  I'm
> a bit surprised to see them summed; is this standard?
>

IIRC, I first saw it in *Numerical Recipes* (1986).

Chuck

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