M(s)stab(L): A Generalization of IDR(s)stab(L) for Sequences of Linear Systems

TL;DR

Mstab is a new Krylov subspace recycling method that generalizes IDRstab for efficiently solving sequences of linear systems with fixed matrices but different right-hand sides, outperforming IDRstab in such cases.

Contribution

Mstab introduces a straightforward generalization of IDRstab, extending its applicability to sequences of linear systems with improved efficiency.

Findings

Mstab solves sequences faster than IDRstab.

For a single system, Mstab and IDRstab are equivalent.

Numerical experiments validate Mstab's efficiency.

Abstract

We propose Mstab, a novel Krylov subspace recycling method for the iterative solution of sequences of linear systems with fixed system matrix and changing right-hand sides. This new method is a straight and simple generalization of IDRstab. IDRstab in turn is a very efficient method and generalization of BiCGStab. The theory of Mstab is based on a generalization of the IDR theorem and Sonneveld spaces. Numerical experiments indicate that Mstab can solve sequences of linear systems faster than its corresponding IDRstab variant. Instead, when solving a single system both methods are identical.