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2013

Krylov Subspace Recycling for Sequences of Shifted Linear Systems

Soodhalter, Kirk M., Szyld, Daniel B., Xue, Fei

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We study the use of Krylov subspace recycling for the solution of a sequence of slowly-changing families of linear systems, where each family consists of shifted linear systems that differ in the coefficient matrix only by multiples of the identity.

Our aim is to explore the simultaneous solution of each family of shifted systems within the framework of subspace recycling, using one augmented subspace to extract candidate solutions for all the shifted systems.
The ideal method would use the same augmented subspace for all systems and have fixed storage requirements, independent of the number of shifted systems per family.
We show that a method satisfying both requirements cannot exist in this framework.

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1985
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1989
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1993
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1995
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1996
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