[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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