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

"Stefan van der Walt" <[email protected]> Mon, 01 May 2023 16:20:33 -0700
Newsgroups gmane.comp.python.scientific.devel
Message-ID <[email protected]>
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?

Stéfan

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