Memory-efficient recycling of large Krylov-subspaces for sequences of Hermitian linear systems

2016/04/14 by Neuenhofen, Martin Peter, Groß, Sven
#65F10 #65F50 #65N22 #76M10 #93A15 #93C05 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1604.04052

Abstract

We present a new short-recurrence reaidual-optimal Krylov subspace recycling method for sequences of Hermitian systems of linear equations with a fixed system matrix and changing right-hand sides. Such sequences of linear systems occur while solving, e.g., discretized time-dependent partial differential equations. With this new method it is possible to recycle large-dimensional Krylov-subspaces with smaller computational overhead and storage requirements compared to current Krylov subspace recycling methods as e.g. R-MINRES. In this paper we derive the method from the residual-optimal preconditioned conjugate residual method and duscuss implementation issues. Numerical experiments illustrate the efficiency of our method.

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