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A class of nested iteration schemes for linear systems with a coefficient matrix with a dominant positive definite symmetric part
Axelsson, O; Bai, ZZ; Qiu, SX
2004-04-01
Source PublicationNUMERICAL ALGORITHMS
ISSN1017-1398
Volume35Issue:2-4Pages:351-372
AbstractWe present a class of nested iteration schemes for solving large sparse systems of linear equations with a coefficient matrix with a dominant symmetric positive definite part. These new schemes are actually inner/outer iterations, which employ the classical conjugate gradient method as inner iteration to approximate each outer iterate, while each outer iteration is induced by a convergent and symmetric positive definite splitting of the coefficient matrix. Convergence properties of the new schemes are studied in depth, possible choices of the inner iteration steps are discussed in detail, and numerical examples from the finite-difference discretization of a second-order partial differential equation are used to further examine the effectiveness and robustness of the new schemes over GMRES and its preconditioned variant. Also, we show that the new schemes are, at least, comparable to the variable-step generalized conjugate gradient method and its preconditioned variant.
Keywordsystem of linear equations inner/outer iteration conjugate gradient method Krylov subspace iterations incomplete factorization relaxation iteration convergence theory
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000220453200014
PublisherKLUWER ACADEMIC PUBL
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/1003
Collection计算数学与科学工程计算研究所
Corresponding AuthorAxelsson, O
Affiliation1.Catholic Univ Nijmegen, Fac Math & Informat, NL-6525 ED Nijmegen, Netherlands
2.Chinese Acad Sci, State Key Lab Sci Engn Comp, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100080, Peoples R China
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Axelsson, O,Bai, ZZ,Qiu, SX. A class of nested iteration schemes for linear systems with a coefficient matrix with a dominant positive definite symmetric part[J]. NUMERICAL ALGORITHMS,2004,35(2-4):351-372.
APA Axelsson, O,Bai, ZZ,&Qiu, SX.(2004).A class of nested iteration schemes for linear systems with a coefficient matrix with a dominant positive definite symmetric part.NUMERICAL ALGORITHMS,35(2-4),351-372.
MLA Axelsson, O,et al."A class of nested iteration schemes for linear systems with a coefficient matrix with a dominant positive definite symmetric part".NUMERICAL ALGORITHMS 35.2-4(2004):351-372.
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