Provide a general eigen solver

[rveltz]

Hi,

I maybe asking too much but given the performances of the library, I would be extremely happy to have a general eigen solver.

Thank you for your efforts!!

Romain

I routinely use KrylovKit.eigsolve but I am expecting a nice speedup from Krylov.jl. I can test but your code.

[rveltz]

gentle reminder :D

[amontoison]

@rveltz Do you have one method of eigen solver in mind that will be useful / relevant for you?

[rveltz]

I am looking for a method that works for general operators, eg. no assumption f symmetry nor positivity. The arnoldi algo would be a good start I would say. But maybe it would be redundant with ArnoldiMethod.jl?

[amontoison]

I checked a little bit online what I need to implement for eigen solvers and I have already many bricks in Krylov.jl.
I can reuse the functions for the Krylov processes:
https://jso.dev/Krylov.jl/dev/processes/

Compared to ArnoldiMethod.jl, I have more processes so I can exploit the symmetry if I want also or do a singular value solver with the Golub-Kahan process.

I can have a look after the visit of JB-Caillau at Argonne (in two weeks).

[rveltz]

Great!!!