Spectral properties of a class of matrix splitting preconditioners for saddle point problems

Rui Rui Wang; Qiang Niu; Fei Ma; Lin Zhang Lu

doi:10.1016/j.cam.2015.12.007

Spectral properties of a class of matrix splitting preconditioners for saddle point problems

Rui Rui Wang
, Qiang Niu^*
, Fei Ma
, Lin Zhang Lu

^*Corresponding author for this work

Department of Applied Mathematics

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

Based on the accelerated Hermitian and skew-Hermitian splitting iteration scheme (Bai and Golub, 2007), we propose a new two-parameter matrix splitting preconditioner in this paper. Spectral properties of the preconditioned matrix are analyzed in detail. Furthermore, based on this preconditioner, an improved version of matrix splitting preconditioner is presented and analyzed. Finally, performance of the preconditioners is compared by using GMRES(m) as an iterative solver on linear systems arising from the discretization of Stokes and Navier-Stokes equations.

Original language	English
Pages (from-to)	138-151
Number of pages	14
Journal	Journal of Computational and Applied Mathematics
Volume	298
DOIs	https://doi.org/10.1016/j.cam.2015.12.007
Publication status	Published - 15 May 2016

Keywords

GMRES
Matrix splitting iteration
Preconditioner
Saddle point problem

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10.1016/j.cam.2015.12.007

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title = "Spectral properties of a class of matrix splitting preconditioners for saddle point problems",

abstract = "Based on the accelerated Hermitian and skew-Hermitian splitting iteration scheme (Bai and Golub, 2007), we propose a new two-parameter matrix splitting preconditioner in this paper. Spectral properties of the preconditioned matrix are analyzed in detail. Furthermore, based on this preconditioner, an improved version of matrix splitting preconditioner is presented and analyzed. Finally, performance of the preconditioners is compared by using GMRES(m) as an iterative solver on linear systems arising from the discretization of Stokes and Navier-Stokes equations.",

keywords = "GMRES, Matrix splitting iteration, Preconditioner, Saddle point problem",

author = "Wang, \{Rui Rui\} and Qiang Niu and Fei Ma and Lu, \{Lin Zhang\}",

year = "2016",

month = may,

day = "15",

doi = "10.1016/j.cam.2015.12.007",

language = "English",

volume = "298",

pages = "138--151",

journal = "Journal of Computational and Applied Mathematics",

issn = "0377-0427",

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TY - JOUR

T1 - Spectral properties of a class of matrix splitting preconditioners for saddle point problems

AU - Wang, Rui Rui

AU - Niu, Qiang

AU - Ma, Fei

AU - Lu, Lin Zhang

PY - 2016/5/15

Y1 - 2016/5/15

N2 - Based on the accelerated Hermitian and skew-Hermitian splitting iteration scheme (Bai and Golub, 2007), we propose a new two-parameter matrix splitting preconditioner in this paper. Spectral properties of the preconditioned matrix are analyzed in detail. Furthermore, based on this preconditioner, an improved version of matrix splitting preconditioner is presented and analyzed. Finally, performance of the preconditioners is compared by using GMRES(m) as an iterative solver on linear systems arising from the discretization of Stokes and Navier-Stokes equations.

AB - Based on the accelerated Hermitian and skew-Hermitian splitting iteration scheme (Bai and Golub, 2007), we propose a new two-parameter matrix splitting preconditioner in this paper. Spectral properties of the preconditioned matrix are analyzed in detail. Furthermore, based on this preconditioner, an improved version of matrix splitting preconditioner is presented and analyzed. Finally, performance of the preconditioners is compared by using GMRES(m) as an iterative solver on linear systems arising from the discretization of Stokes and Navier-Stokes equations.

KW - GMRES

KW - Matrix splitting iteration

KW - Preconditioner

KW - Saddle point problem

UR - https://www.scopus.com/pages/publications/84952004392

U2 - 10.1016/j.cam.2015.12.007

DO - 10.1016/j.cam.2015.12.007

M3 - Article

AN - SCOPUS:84952004392

SN - 0377-0427

VL - 298

SP - 138

EP - 151

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

ER -

Spectral properties of a class of matrix splitting preconditioners for saddle point problems

Abstract

Keywords

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