MINRES Seed Projection Methods for Solving Symmetric Linear Systems with Multiple Right-Hand Sides

MINRES Seed Projection Methods for Solving Symmetric Linear Systems with Multiple Right-Hand Sides

We consider the MINRES seed projection method for solving multiple right-hand side linear systems AX=B, where A∈Rn×n is a nonsingular symmetric matrix, B∈Rn×p. In general, GMRES seed projection method is one of the effective methods for solving multiple right-hand side linear systems. However, when...

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Main Authors: Xin Li, Hao Liu, Jingfu Zhu
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2014/357874
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spelling doaj-1e6b8460716241239a042f072d3bad822020-11-24T21:20:05ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472014-01-01201410.1155/2014/357874357874MINRES Seed Projection Methods for Solving Symmetric Linear Systems with Multiple Right-Hand SidesXin Li0Hao Liu1Jingfu Zhu2College of Science, Heilongjiang Bayi Agricultural University, Daqing 163319, ChinaCollege of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, ChinaCollege of Information Technology, Heilongjiang Bayi Agricultural University, Daqing 163319, ChinaWe consider the MINRES seed projection method for solving multiple right-hand side linear systems AX=B, where A∈Rn×n is a nonsingular symmetric matrix, B∈Rn×p. In general, GMRES seed projection method is one of the effective methods for solving multiple right-hand side linear systems. However, when the coefficient matrix is symmetric, the efficiency of this method would be weak. MINRES seed projection method for solving symmetric systems with multiple right-hand sides is proposed in this paper, and the residual estimation is analyzed. The numerical examples show the efficiency of this method.http://dx.doi.org/10.1155/2014/357874
collection DOAJ
language English
format Article
sources DOAJ
author Xin Li
Hao Liu
Jingfu Zhu
spellingShingle Xin Li
Hao Liu
Jingfu Zhu
MINRES Seed Projection Methods for Solving Symmetric Linear Systems with Multiple Right-Hand Sides
Mathematical Problems in Engineering
author_facet Xin Li
Hao Liu
Jingfu Zhu
author_sort Xin Li
title MINRES Seed Projection Methods for Solving Symmetric Linear Systems with Multiple Right-Hand Sides
title_short MINRES Seed Projection Methods for Solving Symmetric Linear Systems with Multiple Right-Hand Sides
title_full MINRES Seed Projection Methods for Solving Symmetric Linear Systems with Multiple Right-Hand Sides
title_fullStr MINRES Seed Projection Methods for Solving Symmetric Linear Systems with Multiple Right-Hand Sides
title_full_unstemmed MINRES Seed Projection Methods for Solving Symmetric Linear Systems with Multiple Right-Hand Sides
title_sort minres seed projection methods for solving symmetric linear systems with multiple right-hand sides
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2014-01-01
description We consider the MINRES seed projection method for solving multiple right-hand side linear systems AX=B, where A∈Rn×n is a nonsingular symmetric matrix, B∈Rn×p. In general, GMRES seed projection method is one of the effective methods for solving multiple right-hand side linear systems. However, when the coefficient matrix is symmetric, the efficiency of this method would be weak. MINRES seed projection method for solving symmetric systems with multiple right-hand sides is proposed in this paper, and the residual estimation is analyzed. The numerical examples show the efficiency of this method.
url http://dx.doi.org/10.1155/2014/357874
work_keys_str_mv AT xinli minresseedprojectionmethodsforsolvingsymmetriclinearsystemswithmultiplerighthandsides
AT haoliu minresseedprojectionmethodsforsolvingsymmetriclinearsystemswithmultiplerighthandsides
AT jingfuzhu minresseedprojectionmethodsforsolvingsymmetriclinearsystemswithmultiplerighthandsides
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