[petsc-users] Computing Krylov decompositions with PETSc/SLEPc

Gard Spreemann gard.spreemann at epfl.ch
Fri Jul 6 09:00:05 CDT 2018

Hello list,

It is my (naive) understanding that a lot of the eigenproblem solvers
in SLEPc and linear solvers in PETSc use Krylov subspace methods
internally. However, I can't seem to find any functionality in
either library that exposes these underlying methods.

Specifically, I'm looking for something that takes

 - a sparse symmetric real NxN matrix A (or a function for computing
   matrix-vector products with A)

 - a real vector x of size N

 - a (typically small) integer M<=N

and returns an orthonormal basis v_1,…,v_M for

 span(x, Ax, A^2x, …, A^{M-1}x)

so that V^T A V is tridiagonal, where V is the matrix with v_1,…,v_M
as columns.

Am I overlooking something, misunderstanding something, or something
else? Any help is greatly appreciated (even if it involves pointing me
to a different library).

I'm sorry if the question is ill-posed, I am not well-versed in
numerical linear algebra.

Thanks in advance.

 Best regards,
 Gard Spreemann

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