Adding GMRES to iterative_solvers Module

[AlexanderGSC]

Motivation

Hi,

I’ve been taking a look at the stdlib_linalg_iterative_solvers module and noticed that there isn’t an implementation of GMRES. Would this be a worthwhile addition to the stdlib? If so, I’d be happy to help; I have some implementations that I can adapt.

Motivation: GMRES is one of the most widely used iterative methods: compared to bicgstab, it offers improved robustness, but it has the drawback of consuming significantly more memory (the Krylov basis requires m vectors of size n, where n is the problem size and m is the restart size).

Prior Art

No response

Additional Information

No response

[jvdp1]

Would this be a worthwhile addition to the stdlib?

Thank you for the proposal. Yes, it will be a nice addition to stdlib. Feel free to open a PR, inspired by other CG methods in stdlib.

[jalvesz]

I had started a branch to work on that and was planning to polish it later on: https://github.com/jalvesz/stdlib/tree/gmres

If you would like, it would be nice to collaborate on that. Feel free to adapt/mix with your own ideas.

@loiseaujc also had some ideas for this inspired by his project https://github.com/nekStab/LightKrylov

[AlexanderGSC]

Hello! Thank you very much for your replies.

I’ve had a look at @jalvesz’s GMRES branch and it’s helped me understand how gmres might fit into the module’s current structure. I’d love to collaborate on this.

Before moving on to a pull request, I think it would be useful to agree on some design details, just to make sure we’re on the same page.

If that’s OK with you, I can open a discussion thread on the fork so we can go over the technical aspects there. Once everything’s agreed, we can work together on a PR.

Best regards

[jalvesz]

Perfect @AlexanderGSC looking forward!