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Solving shifted linear systems with restarted GMRES augmented with error approximations.

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Title: Solving shifted linear systems with restarted GMRES augmented with error approximations.
Authors: Wang, Rui-Rui1 (AUTHOR), Niu, Qiang2 (AUTHOR), Tang, Xiao-Bin3 (AUTHOR), Wang, Xiang1,4 (AUTHOR) wangxiang49@ncu.edu.cn
Source: Computers & Mathematics with Applications. Sep2019, Vol. 78 Issue 6, p1910-1918. 9p.
Subjects: Approximation error, Shift systems, Linear systems, Krylov subspace, Canning & preserving
Abstract: In this paper, we investigate a variant of the restarted GMRES method for solving a series of large sparse linear systems. Restarting is carried out by augmenting Krylov subspaces with some recently generated error approximations from the seed system. The method can preserve a nice property that allows solving the seed and the added linear systems at the cost of only one matrix–vector multiplication per iteration. Compared with solving each added linear system separately, the advantage of the new scheme is to lower down the overall cost of solving all added linear systems. Numerical experiments illustrate the efficiency of the acceleration strategy. [ABSTRACT FROM AUTHOR]
Copyright of Computers & Mathematics with Applications is the property of Pergamon Press - An Imprint of Elsevier Science 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.)
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Header DbId: egs
DbLabel: Engineering Source
An: 138156269
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PubType: Academic Journal
PubTypeId: academicJournal
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  Data: Solving shifted linear systems with restarted GMRES augmented with error approximations.
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  Data: <searchLink fieldCode="AR" term="%22Wang%2C+Rui-Rui%22">Wang, Rui-Rui</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Niu%2C+Qiang%22">Niu, Qiang</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Tang%2C+Xiao-Bin%22">Tang, Xiao-Bin</searchLink><relatesTo>3</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Wang%2C+Xiang%22">Wang, Xiang</searchLink><relatesTo>1,4</relatesTo> (AUTHOR)<i> wangxiang49@ncu.edu.cn</i>
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  Data: <searchLink fieldCode="JN" term="%22Computers+%26+Mathematics+with+Applications%22">Computers & Mathematics with Applications</searchLink>. Sep2019, Vol. 78 Issue 6, p1910-1918. 9p.
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  Data: <searchLink fieldCode="DE" term="%22Approximation+error%22">Approximation error</searchLink><br /><searchLink fieldCode="DE" term="%22Shift+systems%22">Shift systems</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+systems%22">Linear systems</searchLink><br /><searchLink fieldCode="DE" term="%22Krylov+subspace%22">Krylov subspace</searchLink><br /><searchLink fieldCode="DE" term="%22Canning+%26+preserving%22">Canning & preserving</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: In this paper, we investigate a variant of the restarted GMRES method for solving a series of large sparse linear systems. Restarting is carried out by augmenting Krylov subspaces with some recently generated error approximations from the seed system. The method can preserve a nice property that allows solving the seed and the added linear systems at the cost of only one matrix–vector multiplication per iteration. Compared with solving each added linear system separately, the advantage of the new scheme is to lower down the overall cost of solving all added linear systems. Numerical experiments illustrate the efficiency of the acceleration strategy. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Computers & Mathematics with Applications is the property of Pergamon Press - An Imprint of Elsevier Science 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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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1016/j.camwa.2019.03.037
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      – Code: eng
        Text: English
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        PageCount: 9
        StartPage: 1910
    Subjects:
      – SubjectFull: Approximation error
        Type: general
      – SubjectFull: Shift systems
        Type: general
      – SubjectFull: Linear systems
        Type: general
      – SubjectFull: Krylov subspace
        Type: general
      – SubjectFull: Canning & preserving
        Type: general
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      – TitleFull: Solving shifted linear systems with restarted GMRES augmented with error approximations.
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            NameFull: Wang, Rui-Rui
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            NameFull: Niu, Qiang
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            NameFull: Tang, Xiao-Bin
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            – D: 15
              M: 09
              Text: Sep2019
              Type: published
              Y: 2019
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            – TitleFull: Computers & Mathematics with Applications
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