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

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Title: Spectral properties of a class of matrix splitting preconditioners for saddle point problems.
Authors: Wang, Rui-Rui1, Niu, Qiang2 kangniu@gmail.com, Ma, Fei2, Lu, Lin-Zhang3,4
Source: Journal of Computational & Applied Mathematics. May2016, Vol. 298, p138-151. 14p.
Subjects: Spectral theory, Set theory, Matrices (Mathematics), Saddlepoint approximations, Iterative methods (Mathematics), Linear systems, Discretization methods, Navier-Stokes equations
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. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Computational & Applied Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 112366926
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PubTypeId: academicJournal
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  Data: Spectral properties of a class of matrix splitting preconditioners for saddle point problems.
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  Data: <searchLink fieldCode="AR" term="%22Wang%2C+Rui-Rui%22">Wang, Rui-Rui</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Niu%2C+Qiang%22">Niu, Qiang</searchLink><relatesTo>2</relatesTo><i> kangniu@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Ma%2C+Fei%22">Ma, Fei</searchLink><relatesTo>2</relatesTo><br /><searchLink fieldCode="AR" term="%22Lu%2C+Lin-Zhang%22">Lu, Lin-Zhang</searchLink><relatesTo>3,4</relatesTo>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Computational+%26+Applied+Mathematics%22">Journal of Computational & Applied Mathematics</searchLink>. May2016, Vol. 298, p138-151. 14p.
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  Data: <searchLink fieldCode="DE" term="%22Spectral+theory%22">Spectral theory</searchLink><br /><searchLink fieldCode="DE" term="%22Set+theory%22">Set theory</searchLink><br /><searchLink fieldCode="DE" term="%22Matrices+%28Mathematics%29%22">Matrices (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Saddlepoint+approximations%22">Saddlepoint approximations</searchLink><br /><searchLink fieldCode="DE" term="%22Iterative+methods+%28Mathematics%29%22">Iterative methods (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+systems%22">Linear systems</searchLink><br /><searchLink fieldCode="DE" term="%22Discretization+methods%22">Discretization methods</searchLink><br /><searchLink fieldCode="DE" term="%22Navier-Stokes+equations%22">Navier-Stokes equations</searchLink>
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  Label: Abstract
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  Data: 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. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Computational & Applied Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1016/j.cam.2015.12.007
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      – Code: eng
        Text: English
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        PageCount: 14
        StartPage: 138
    Subjects:
      – SubjectFull: Spectral theory
        Type: general
      – SubjectFull: Set theory
        Type: general
      – SubjectFull: Matrices (Mathematics)
        Type: general
      – SubjectFull: Saddlepoint approximations
        Type: general
      – SubjectFull: Iterative methods (Mathematics)
        Type: general
      – SubjectFull: Linear systems
        Type: general
      – SubjectFull: Discretization methods
        Type: general
      – SubjectFull: Navier-Stokes equations
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      – TitleFull: Spectral properties of a class of matrix splitting preconditioners for saddle point problems.
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            NameFull: Ma, Fei
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              Text: May2016
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