Referring to Krylov Subspaces and the methods of solutions to linear systems of equations which exploit these spaces.
Questions tagged [krylov-method]
80 questions
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How do low rank modifications affect Krylov method convergence?
Say I have a linear system $A x = b$, which converges quickly using a suitable Krylov method (such as CG or GMRES) for all $b$. If $B$ is a matrix with low rank $r$, will the same Krylov method on the system $(A + B) x = b$ also converge quickly…
Geoffrey Irving
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Why is pinning a point to remove a null space bad?
A Poisson equation with all Neumann boundary conditions has a single constant dimensional null space. When solving via a Krylov method, the null space can be removed either by subtracting the mean of the solution each iteration or by pinning the…
Geoffrey Irving
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Looking for a specific version of the Quasi-Minimal Residual (QMR) method
I'm looking for an alternative formulation of Quasi-Minimal Residual (QMR) from Freund and Nachtigal (1994) based on a Lanczos process for complex valued matrices based on $A^H$ instead of $A^T$.
Specifically, I'm not quite sure how algorithm 7.1…
