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Persistent URL http://purl.org/net/epubs/work/65300
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Record Id 65300
Title On positive semidefinite modification schemes for incomplete Cholesky factorization
Abstract Incomplete Cholesky factorizations have long been important as preconditioners for use in solving largescale symmetric positive-definite linear systems. In this paper, we present a brief historical overview of the work that has been done over the last fifty years, highlighting key discoveries and rediscoveries. We focus in particular on the relationship between two important positive semide nite modification schemes,namely that of Jennings and Malik and that of Tismenetsky. We present a novel view of their relationship 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. The experiments are used to isolate the effects of semidefinite modifications to enable their usefulness in the development of robust algebraic incomplete factorization preconditioners to be assessed. We show that we are able to compute sparse incomplete factors that provide robust, general-purpose preconditioners.
Organisation STFC , SCI-COMP
Keywords positive-definite symmetric systems , incomplete Cholesky factorization , iterative solvers , preconditioning , sparse linear systems , sparse matrices
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Language English (EN)
Type Details URI(s) Local file(s) Year
Report RAL Preprints RAL-P-2013-005. 2013. RAL-P-2013-005.pdf 2013
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