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

	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
发表期刊	NUMERICAL ALGORITHMS
ISSN	1017-1398
卷号	35 期号:2-4 页码:351-372
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.
关键词	system of linear equations inner/outer iteration conjugate gradient method Krylov subspace iterations incomplete factorization relaxation iteration convergence theory
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000220453200014
出版者	KLUWER ACADEMIC PUBL
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/1003
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.