Modified incomplete factorization strategies

Beauwens, Robert

doi:10.1007/bfb0090898

Cited by 22 publications

(22 citation statements)

References 11 publications

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“…If A is a symmetric and positive-definite M-matrix, then the theory of modified incomplete factorizations may be extended based on Mmatrix properties and matching (or nearly matching) a given positive vector (such as the eigenvector of the M-matrix, A, corresponding to its smallest eigenvalue) [2].…”

Section: Complex Modificationmentioning

confidence: 99%

Modification and Compensation Strategies for Threshold-based Incomplete Factorizations

MacLachlan¹,

Osei-Kuffuor²,

Saad³

2012

SIAM J. Sci. Comput.

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Abstract. Standard (single-level) incomplete factorization preconditioners are known to successfully accelerate Krylov subspace iterations for many linear systems. The classical Modified Incomplete LU (MILU) factorization approach improves the acceleration given by (standard) ILU approaches, by modifying the non-unit diagonal in the factorization to match the action of the system matrix on a given vector, typically the constant vector. Here, we examine the role of similar modifications within the dual-threshold ILUT algorithm. We introduce column and row variants of the modified ILUT algorithm and discuss optimal ways of modifying the columns or rows of the computed factors to improve their accuracy and stability. Modifications are considered for both the diagonal and offdiagonal entries of the factors, based on one or many vectors, chosen a priori or through an Arnoldi iteration. Numerical results are presented to support our findings.

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Section: Complex Modificationmentioning

confidence: 99%

Modification and Compensation Strategies for Threshold-based Incomplete Factorizations

MacLachlan¹,

Osei-Kuffuor²,

Saad³

2012

SIAM J. Sci. Comput.

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“…Another point which deserves to be explored is the usage of other variants of the basic IC (see, e.g. References [28,29,36,46,35,40]). …”

Section: Discussionmentioning

confidence: 99%

“…We shall use h;i = 0, which in general gives rise to accurate estimates (see, e.g. References [36] for i = 1, and Reference [40, Section 5] for in).…”

Section: Spectral Analysismentioning

confidence: 99%

Spectral analysis of parallel incomplete factorizations with implicit pseudo‐overlap

Made

Vorst

2001

Numerical Linear Algebra App

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SUMMARYTwo general parallel incomplete factorization strategies are investigated. The techniques may be interpreted as generalized domain decomposition methods. In contrast to classical domain decomposition methods, adjacent subdomains exchange data during the construction of the incomplete factorization matrix, as well as during each local forward elimination and each local backward elimination involved in the application of the preconditioner. Local renumberings of nodes are combined with suitable global ÿll-in strategy in an (successful) attempt to overcome the well-known trade-o between high parallelism (locality) and fast convergence (globality). From an algebraic viewpoint, our techniques may be implemented as global renumbering strategies. Theoretical spectral analysis is provided, which displays that the convergence rate weakly depends on the number of subdomains. Numerical results obtained on a 16-processor SGI Origin 2000 are reported, showing the e ciency of our parallel preconditionings.

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“…According as A = 0 or not, one speaks of unperturbed or perturbed strategies [8]. The first case corresponds to none other than the popular generalized row sum criterion variant of modified methods.…”

Section: Modified Incomplete Block Factorizationsmentioning

confidence: 99%