On Positive Semidefinite Modification Schemes for Incomplete Cholesky Factorization
Abstract
Incomplete Cholesky factorizations have long been important as preconditioners for use in solving large-scale symmetric positive-definite linear systems. In this paper, we focus on the relationship between two important positive semidefinite modification schemes that were introduced to avoid factorization breakdown, namely, the approach of Jennings and Malik and that of Tismenetsky. We present a novel view of the relationship between the two schemes and implement them in combination with a limited memory approach. We explore their effectiveness using extensive numerical experiments involving a large set of test problems arising from a wide range of practical applications.
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Information & Authors
Information
Published In
SIAM Journal on Scientific Computing
Pages: A609 - A633
DOI: 10.1137/130917582
ISSN (online): 1095-7197
Copyright
© 2014, Society for Industrial and Applied Mathematics.
History
Submitted: 18 April 2013
Accepted: 13 December 2013
Published online: 8 April 2014
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