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SIAM J. on Scientific Computing / Volume 28 / Issue 5

SIAM J. Sci. Comput. 28, pp. 1651-1674 (24 pages)

Recycling Krylov Subspaces for Sequences of Linear Systems

Michael L. Parks, Eric de Sturler, Greg Mackey, Duane D. Johnson, and Spandan Maiti

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Many problems in science and engineering require the solution of a long sequence of slowly changing linear systems. We propose and analyze two methods that significantly reduce the total number of matrix‐vector products required to solve all systems. We consider the general case where both the matrix and right‐hand side change, and we make no assumptions regarding the change in the right‐hand sides. Furthermore, we consider general nonsingular matrices, and we do not assume that all matrices are pairwise close or that the sequence of matrices converges to a particular matrix. Our methods work well under these general assumptions, and hence form a significant advancement with respect to related work in this area. We can reduce the cost of solving subsequent systems in the sequence by recycling selected subspaces generated for previous systems. We consider two approaches that allow for the continuous improvement of the recycled subspace at low cost. We consider both Hermitian and non‐Hermitian problems, and we analyze our algorithms both theoretically and numerically to illustrate the effects of subspace recycling. We also demonstrate the effectiveness of our algorithms for a range of applications from computational mechanics, materials science, and computational physics.

© 2006 Society for Industrial and Applied Mathematics

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KEYWORDS

AMS Subject Headings

65F10, 65N22

PUBLICATION DATA

ISSN

1064-8275 (print)  
1095-7197 (online)

Publisher

$abstract.society.value is a Member of CrossRef Society for Industrial and Applied Mathematics

ARTICLE DATA

History
Received April 24, 2004
Accepted February 16, 2006
Published online October 06, 2006
Digital Object Identifier
http://dx.doi.org/10.1137/040607277

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