Accelerate weighted GMRES by augmenting error approximations

Qiang Niu; Linzhang Lu; Jituan Zhou

doi:10.1080/00207160802617004

Accelerate weighted GMRES by augmenting error approximations

Qiang Niu^*
, Linzhang Lu
, Jituan Zhou

^*Corresponding author for this work

Xiamen University
Guizhou Normal University
Wuyi University

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

3 Citations (Scopus)

Abstract

By augmenting error approximations at every restart cycle, this paper presents an accelerating strategy for restarted weighted generalized minimum residual (GMRES) method. We show that the procedure can effectively correct the occurrence of small skip D-angles, which indicates a slow convergent phase. Numerical results show that the new method converges much regular and faster than the weighted GMRES method. Finally, comparisons are made between the new and the recently proposed LGMRES methods.

Original language	English
Pages (from-to)	2101-2112
Number of pages	12
Journal	International Journal of Computer Mathematics
Volume	87
Issue number	9
DOIs	https://doi.org/10.1080/00207160802617004
Publication status	Published - Jul 2010
Externally published	Yes

Keywords

Arnoldi process
GMRES
WGMRES
iterative method
linear systems

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10.1080/00207160802617004

Cite this

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title = "Accelerate weighted GMRES by augmenting error approximations",

abstract = "By augmenting error approximations at every restart cycle, this paper presents an accelerating strategy for restarted weighted generalized minimum residual (GMRES) method. We show that the procedure can effectively correct the occurrence of small skip D-angles, which indicates a slow convergent phase. Numerical results show that the new method converges much regular and faster than the weighted GMRES method. Finally, comparisons are made between the new and the recently proposed LGMRES methods.",

keywords = "Arnoldi process, GMRES, WGMRES, iterative method, linear systems",

author = "Qiang Niu and Linzhang Lu and Jituan Zhou",

note = "Funding Information: The authors thank the anonymous referees for their valuable comments on how to improve the presentation. This work was supported by the National Natural Science Foundation of China, nos. 10531080. The first author was supported by the China Scholarship Council.",

year = "2010",

month = jul,

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volume = "87",

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T1 - Accelerate weighted GMRES by augmenting error approximations

AU - Niu, Qiang

AU - Lu, Linzhang

AU - Zhou, Jituan

N1 - Funding Information: The authors thank the anonymous referees for their valuable comments on how to improve the presentation. This work was supported by the National Natural Science Foundation of China, nos. 10531080. The first author was supported by the China Scholarship Council.

PY - 2010/7

Y1 - 2010/7

N2 - By augmenting error approximations at every restart cycle, this paper presents an accelerating strategy for restarted weighted generalized minimum residual (GMRES) method. We show that the procedure can effectively correct the occurrence of small skip D-angles, which indicates a slow convergent phase. Numerical results show that the new method converges much regular and faster than the weighted GMRES method. Finally, comparisons are made between the new and the recently proposed LGMRES methods.

AB - By augmenting error approximations at every restart cycle, this paper presents an accelerating strategy for restarted weighted generalized minimum residual (GMRES) method. We show that the procedure can effectively correct the occurrence of small skip D-angles, which indicates a slow convergent phase. Numerical results show that the new method converges much regular and faster than the weighted GMRES method. Finally, comparisons are made between the new and the recently proposed LGMRES methods.

KW - Arnoldi process

KW - GMRES

KW - WGMRES

KW - iterative method

KW - linear systems

UR - https://www.scopus.com/pages/publications/77954896153

U2 - 10.1080/00207160802617004

DO - 10.1080/00207160802617004

M3 - Article

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VL - 87

SP - 2101

EP - 2112

JO - International Journal of Computer Mathematics

JF - International Journal of Computer Mathematics

IS - 9

ER -

Accelerate weighted GMRES by augmenting error approximations

Abstract

Keywords

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