Alexis Montoison

[documentation] Add a page about the foundations of Krylov methods

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I could give a link to this page to justify my message in this discussion: https://discourse.julialang.org/t/how-to-solve-this-ax-b-faster/81693/22

All Krylov processes can use 5-argument mul!. We should update our Krylov methods to reduce memory requirements. ### Lanczos process - [ ] SYMMLQ - [ ] CG-LANCZOS - [...

USYMLQR

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It will be great to have this method for solving saddle-point and SQD systems. It will also complete the family of "LQR" methods with BiLQR and TriLQR. A basic functional...

[documentation] Matrix-vector products on multiple GPUs

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Example for dense matrices: https://github.com/JuliaGPU/CUDA.jl/pull/918 We should be able to do a similar example for sparse matrices.

Broadcast is not completely optimized on GPU (#242) but it could give some performance benefit by combining multiple CUBLAS calls into a single kernel in the future. Broadcast allows the...

Add documentation about preconditioners

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It will be useful to show how to build relevant preconditioners for our Krylov methods in the documentation with the help of linear operators. - Jacobi - SPAI - Incomplete...

With the trick found for storing vₖ in MINRES-QLP (#200), we should be able to add preconditioning in elliptic norms for USYMLQ and USYMQR.

I should add these functions [here](https://juliasmoothoptimizers.github.io/Krylov.jl/dev/inplace/) and explain that it's not always the exact number of operator-vector products (small difference of 1 matvec).