2014
DOI: 10.1137/130917582
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On Positive Semidefinite Modification Schemes for Incomplete Cholesky Factorization

Abstract: 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 me… Show more

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Cited by 25 publications
(34 citation statements)
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“…[33]. HSL MI35 implements a limited memory IC algorithm (see [46,45] for details). Note that it handles ordering for sparsity and scaling.…”
Section: End Domentioning
confidence: 99%
“…[33]. HSL MI35 implements a limited memory IC algorithm (see [46,45] for details). Note that it handles ordering for sparsity and scaling.…”
Section: End Domentioning
confidence: 99%
“…Incomplete Cholesky (IC) factorizations have long been used as preconditioners for the numerical solution of large sparse, symmetric positive definite linear systems of equations; for an introduction and overview see, for example, [2,46,51] and the many references therein. More recently, a number of authors have considered incomplete LDL T factorizations of symmetric quasi-definite matrices [39], saddle-point systems [52], and general indefinite systems [22,53].…”
Section: C321mentioning
confidence: 99%
“…Over the years, a wealth of different IC variants have been proposed, including structure-based methods, those based on dropping entries below a prescribed threshold, and those based on prescribing the maximum number of entries allowed in L (see, for instance, [2,46,51] and the references therein). Level-based methods (IC(k)) that are based on the sparsity pattern of A plus a small number of levels of fill are popular and straightforward to implement.…”
Section: Incomplete Factorization Of the Normal Matrix Cmentioning
confidence: 99%
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“…This preconditioner is obtained by computing a direct LU factorization of the matrix A, and by dropping some of the elements during the decomposition, based on either their numerical value or their relation with respect to the graph of the input matrix A [28,30]. For a historical overview on preconditioning techniques and incomplete factorizations, refer to [4,32].…”
mentioning
confidence: 99%