Threshold incomplete factorization constraint preconditioners for saddle-point matrices

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1 Citation (Scopus)

Abstract

This paper presents a drop-threshold incomplete LD-1LT (δ) factorization constraint preconditioner for saddle-point systems using a threshold parameter δ. A transformed saddle-point matrix is partitioned into a block structure with blocks of order 1 and 2 constituting ‘a priori pivots’. Based on these pivots an incomplete LD-1LT (δ) factorization constraint preconditioner is computed that approaches an exact form as δ approaches zero. We prove that both the exact and incomplete factorizations exist such that the entries of the constraint block remain unaltered in the triangular factors. Numerical results are presented for validation.
LanguageEnglish
Pages76-107
Number of pages32
JournalLinear Algebra and Its Applications
Volume545
Issue numberMay 2018
DOIs
StatePublished - 15 May 2018

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Incomplete Factorization
Saddlepoint
Factorization
Preconditioner
Pivot
Saddle Point Systems
Threshold Parameter
Block Structure
Triangular
Numerical Results
Zero

Keywords

  • Saddle-point matrices; Transformation; Incomplete factorization; Constraint preconditioner

Cite this

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title = "Threshold incomplete factorization constraint preconditioners for saddle-point matrices",
abstract = "This paper presents a drop-threshold incomplete LD-1LT (δ) factorization constraint preconditioner for saddle-point systems using a threshold parameter δ. A transformed saddle-point matrix is partitioned into a block structure with blocks of order 1 and 2 constituting ‘a priori pivots’. Based on these pivots an incomplete LD-1LT (δ) factorization constraint preconditioner is computed that approaches an exact form as δ approaches zero. We prove that both the exact and incomplete factorizations exist such that the entries of the constraint block remain unaltered in the triangular factors. Numerical results are presented for validation.",
keywords = "Saddle-point matrices; Transformation; Incomplete factorization; Constraint preconditioner",
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Threshold incomplete factorization constraint preconditioners for saddle-point matrices. / Lungten, S.; Schilders, W.H.A.; Maubach, J.M.L.

In: Linear Algebra and Its Applications, Vol. 545, No. May 2018, 15.05.2018, p. 76-107.

Research output: Contribution to journalArticleAcademicpeer-review

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AU - Lungten,S.

AU - Schilders,W.H.A.

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N2 - This paper presents a drop-threshold incomplete LD-1LT (δ) factorization constraint preconditioner for saddle-point systems using a threshold parameter δ. A transformed saddle-point matrix is partitioned into a block structure with blocks of order 1 and 2 constituting ‘a priori pivots’. Based on these pivots an incomplete LD-1LT (δ) factorization constraint preconditioner is computed that approaches an exact form as δ approaches zero. We prove that both the exact and incomplete factorizations exist such that the entries of the constraint block remain unaltered in the triangular factors. Numerical results are presented for validation.

AB - This paper presents a drop-threshold incomplete LD-1LT (δ) factorization constraint preconditioner for saddle-point systems using a threshold parameter δ. A transformed saddle-point matrix is partitioned into a block structure with blocks of order 1 and 2 constituting ‘a priori pivots’. Based on these pivots an incomplete LD-1LT (δ) factorization constraint preconditioner is computed that approaches an exact form as δ approaches zero. We prove that both the exact and incomplete factorizations exist such that the entries of the constraint block remain unaltered in the triangular factors. Numerical results are presented for validation.

KW - Saddle-point matrices; Transformation; Incomplete factorization; Constraint preconditioner

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