A parameterized extended shift-splitting preconditioner for nonsymmetric saddle point problems

Seryas Vakili; Ghodrat Ebadi; Cornelis Vuik

doi:10.1002/nla.2478

A parameterized extended shift-splitting preconditioner for nonsymmetric saddle point problems

Seryas Vakili, Ghodrat Ebadi^*, Cornelis Vuik

^*Corresponding author for this work

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Abstract

In this article, a parameterized extended shift-splitting (PESS) method and its induced preconditioner are given for solving nonsingular and nonsymmetric saddle point problems with nonsymmetric positive definite (1,1) part. The convergence analysis of the (Formula presented.) iteration method is discussed. The distribution of eigenvalues of the preconditioned matrix is provided. A number of experiments are given to verify the efficiency of the (Formula presented.) method for solving nonsymmetric saddle-point problems.

Original language	English
Article number	e2478
Number of pages	24
Journal	Numerical Linear Algebra with Applications
Volume	30 (2023)
Issue number	4
DOIs	https://doi.org/10.1002/nla.2478
Publication status	Published - 2022

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Keywords

convergence
preconditioning
saddle point problem
shift-splitting

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10.1002/nla.2478

Numerical Linear Algebra App - 2022 - Vakili - A parameterized extended shift%E2%80%90splitting preconditioner for nonsymmetricFinal published version, 1.71 MB

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abstract = "In this article, a parameterized extended shift-splitting (PESS) method and its induced preconditioner are given for solving nonsingular and nonsymmetric saddle point problems with nonsymmetric positive definite (1,1) part. The convergence analysis of the (Formula presented.) iteration method is discussed. The distribution of eigenvalues of the preconditioned matrix is provided. A number of experiments are given to verify the efficiency of the (Formula presented.) method for solving nonsymmetric saddle-point problems.",

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AU - Vuik, Cornelis

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N2 - In this article, a parameterized extended shift-splitting (PESS) method and its induced preconditioner are given for solving nonsingular and nonsymmetric saddle point problems with nonsymmetric positive definite (1,1) part. The convergence analysis of the (Formula presented.) iteration method is discussed. The distribution of eigenvalues of the preconditioned matrix is provided. A number of experiments are given to verify the efficiency of the (Formula presented.) method for solving nonsymmetric saddle-point problems.

AB - In this article, a parameterized extended shift-splitting (PESS) method and its induced preconditioner are given for solving nonsingular and nonsymmetric saddle point problems with nonsymmetric positive definite (1,1) part. The convergence analysis of the (Formula presented.) iteration method is discussed. The distribution of eigenvalues of the preconditioned matrix is provided. A number of experiments are given to verify the efficiency of the (Formula presented.) method for solving nonsymmetric saddle-point problems.

KW - convergence

KW - preconditioning

KW - saddle point problem

KW - shift-splitting

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JF - Numerical Linear Algebra with Applications

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ER -

A parameterized extended shift-splitting preconditioner for nonsymmetric saddle point problems

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