Accelerated GCRO-DR method for solving sequences of systems of linear equations

Qiang Niu; Lin Zhang Lu; Gang Liu

doi:10.1016/j.cam.2013.04.013

Accelerated GCRO-DR method for solving sequences of systems of linear equations

Qiang Niu^*, Lin Zhang Lu, Gang Liu

^*Corresponding author for this work

Department of Applied Mathematics

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

7 Citations (Scopus)

Abstract

By recycling some error approximations generated during a previous cycle of iterations, we present a technique for improving the convergence of GCRO-DR. The scheme is able to mitigate the occurrence of small skip angles occurring in GCRO-DR, and thus considerably accelerates the convergence. The alternative phenomenon of the residual vectors is examined numerically, and the effectiveness of the new method is illustrated by several examples from practical applications.

Original language	English
Pages (from-to)	131-141
Number of pages	11
Journal	Journal of Computational and Applied Mathematics
Volume	253
DOIs	https://doi.org/10.1016/j.cam.2013.04.013
Publication status	Published - 2013

Keywords

GCRO-DR
GMRES
LGMRES
Preconditioner

Access to Document

10.1016/j.cam.2013.04.013

Cite this

@article{3bf21dca72d64e34905df0d561febf33,

title = "Accelerated GCRO-DR method for solving sequences of systems of linear equations",

abstract = "By recycling some error approximations generated during a previous cycle of iterations, we present a technique for improving the convergence of GCRO-DR. The scheme is able to mitigate the occurrence of small skip angles occurring in GCRO-DR, and thus considerably accelerates the convergence. The alternative phenomenon of the residual vectors is examined numerically, and the effectiveness of the new method is illustrated by several examples from practical applications.",

keywords = "GCRO-DR, GMRES, LGMRES, Preconditioner",

author = "Qiang Niu and Lu, {Lin Zhang} and Gang Liu",

note = "Funding Information: This work is supported by the Research Development Fund (RDF) of XJTLU and the National Science Foundation (NSF) under Grant No. 11261012 . ",

year = "2013",

doi = "10.1016/j.cam.2013.04.013",

language = "English",

volume = "253",

pages = "131--141",

journal = "Journal of Computational and Applied Mathematics",

issn = "0377-0427",

}

TY - JOUR

T1 - Accelerated GCRO-DR method for solving sequences of systems of linear equations

AU - Niu, Qiang

AU - Lu, Lin Zhang

AU - Liu, Gang

N1 - Funding Information: This work is supported by the Research Development Fund (RDF) of XJTLU and the National Science Foundation (NSF) under Grant No. 11261012 .

PY - 2013

Y1 - 2013

N2 - By recycling some error approximations generated during a previous cycle of iterations, we present a technique for improving the convergence of GCRO-DR. The scheme is able to mitigate the occurrence of small skip angles occurring in GCRO-DR, and thus considerably accelerates the convergence. The alternative phenomenon of the residual vectors is examined numerically, and the effectiveness of the new method is illustrated by several examples from practical applications.

AB - By recycling some error approximations generated during a previous cycle of iterations, we present a technique for improving the convergence of GCRO-DR. The scheme is able to mitigate the occurrence of small skip angles occurring in GCRO-DR, and thus considerably accelerates the convergence. The alternative phenomenon of the residual vectors is examined numerically, and the effectiveness of the new method is illustrated by several examples from practical applications.

KW - GCRO-DR

KW - GMRES

KW - LGMRES

KW - Preconditioner

UR - http://www.scopus.com/inward/record.url?scp=84877341912&partnerID=8YFLogxK

U2 - 10.1016/j.cam.2013.04.013

DO - 10.1016/j.cam.2013.04.013

M3 - Article

AN - SCOPUS:84877341912

SN - 0377-0427

VL - 253

SP - 131

EP - 141

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

ER -

Accelerated GCRO-DR method for solving sequences of systems of linear equations

Abstract

Keywords

Access to Document

Other files and links

Cite this