search

RalphAS / PeriodicSchurDecompositions.jl

Julia package for periodic Schur decompositions of matrix products
Other
8 stars 0 forks source link

matrixfree partial_gpschur #8

Closed rveltz closed 1 year ago

rveltz commented 1 year ago

Hi,

Thanks a lot for your work!

Would it make sense to have a Matrix-free generalized periodic Schur decomposition? How would one provide Bₚ⁻¹? Just Bₚ?

Or maybe it is better to use partial_pschur where the user implement x -> B \ A*x?

Thanks for your input

RalphAS commented 1 year ago

I don't know of a Krylov scheme to handle the generalized problem directly. So I'd advise a user-implemented x -> Bₚ \ x at least, to alternate with the Aₚ operators. (It may be more accurate to separate the A and B operations.) Can you afford a sparse direct solver? Otherwise it may be tricky to pick an adequate (but not too expensive) tolerance for an iterative method.

rveltz commented 1 year ago

I thought you could do a gmres given that you have the Krylov infrastructure but you are right, better leave this on the user side