[documentation] KrylovPreconditioners.jl

[amontoison]

I should add a section about the Julia package KrylovPreconditioners.jl and its GPU preconditioners ILU(0), IC(0) and block-Jacobi.

[RoyiAvital]

Examples on how to build a good and simple conditioners will be great.
I can provide an example of a matrix which is used in Image Processing (I don't have a simple conditioner for it, but probably you'd be able to infer one).

[amontoison]

Hi @RoyiAvital! You already have a few examples in section "preconditioners" of the documentation:
https://jso.dev/Krylov.jl/dev/preconditioners/#Examples

[amontoison]

What I would like to add in the documentation is a matrix-free preconditioner but I didn't find a good example yet.
I added operators related to FFT and PDE recently but nothing related to preconditioners:
https://jso.dev/Krylov.jl/dev/matrix_free/

If you have an idea of an application in "image processing", it will be great!

[RoyiAvital]

There are many graph inspired algorithms which generates a large system to solve.
It would be great to have an examples / recipe how to maximize performance to solve those problems.

I can also give a large example of inverse problem where the problem can be solved using operators.
I haven't thought about utilizing the operator approach for their conditioners.

[amontoison]

An example with an inverse problem could be great!

For the preconditioner, I think that an example with a method like SOR ou Gauss-Seidel as preconditioner could be relevant.