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

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.Comment: 21 pages, 8 figures, submitted manuscrip

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS Numer. Linear Algebra Appl. 2009;:1–34 Prepared using nlaauth.cls [Version: 2002/09/18 v1.02] Multisplitting for Regularized Least Squares with Krylov Subspace Recycling

The method of multisplitting, implemented as a restricted additive Schwarz type algorithm, is extended for the solution of regularized least squares problems. The presented non-stationary version of the algorithm uses dynamic updating of the weights applied to the subdomains in reconstituting the global solution. Standard convergence results follow from extensive prior literature on linear multisplitting schemes. Additional convergence results on nonstationary iterations yield convergence conditions for the presented nonstationary multisplitting algorithm. The global iteration uses repeated solves of local problems with changing right hand sides but a fixed system matrix. These problems are solve