A class of nested iteration schemes for linear systems with a coefficient matrix with a dominant positive definite symmetric part

CORC > 数学与系统科学研究院 > 中国科学院数学与系统科学研究院 > 计算数学与科学工程计算研究所

	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
刊名	NUMERICAL ALGORITHMS
	2004-04-01
卷号	35 期号:2-4 页码:351-372
关键词	system of linear equations inner/outer iteration conjugate gradient method Krylov subspace iterations incomplete factorization relaxation iteration convergence theory
ISSN号	1017-1398
英文摘要	We 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.
WOS研究方向	Mathematics
语种	英语
出版者	KLUWER ACADEMIC PUBL
WOS记录号	WOS:000220453200014
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/1002]
专题	计算数学与科学工程计算研究所
通讯作者	Axelsson, O
作者单位	1.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
推荐引用方式 GB/T 7714	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.