A Non-Krylov Subspace Method for Solving Large and Sparse Linear System of Equations

doi:10.4208/nmtma.2016.y14014

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 Non-Krylov Subspace Method for Solving Large and Sparse Linear System of Equations
	Peng, Wujian 1; Lin, Qun2
刊名	NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS
	2016-05-01
卷号	9 期号:2 页码:289-314
关键词	Iterative method accumulated projection Krylov subspace
ISSN号	1004-8979
DOI	10.4208/nmtma.2016.y14014
英文摘要	Most current prevalent iterative methods can be classified into the so-called extended Krylov subspace methods, a class of iterative methods which do not fall into this category are also proposed in this paper. Comparing with traditional Krylov subspace methods which always depend on the matrix-vector multiplication with a fixed matrix, the newly introduced methods (the so-called (progressively) accumulated projection methods, or AP (PAP) for short) use a projection matrix which varies in every iteration to form a subspace from which an approximate solution is sought. More importantly an accelerative approach (called APAP) is introduced to improve the convergence of PAP method. Numerical experiments demonstrate some surprisingly improved convergence behavior. Comparison between benchmark extended Krylov subspace methods (Block Jacobi and GMRES) are made and one can also see remarkable advantage of APAP in some examples. APAP is also used to solve systems with extremely ill-conditioned coefficient matrix (the Hilbert matrix) and numerical experiments shows that it can bring very satisfactory results even when the size of system is up to a few thousands.
WOS研究方向	Mathematics
语种	英语
出版者	CAMBRIDGE UNIV PRESS
WOS记录号	WOS:000377119800007
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/22843]
专题	计算数学与科学工程计算研究所
通讯作者	Peng, Wujian
作者单位	1.Zhaoqing Univ, Dept Math & Stats Sci, Zhaoqing 526061, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100081, Peoples R China
推荐引用方式 GB/T 7714	Peng, Wujian,Lin, Qun. A Non-Krylov Subspace Method for Solving Large and Sparse Linear System of Equations[J]. NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS,2016,9(2):289-314.
APA	Peng, Wujian,&Lin, Qun.(2016).A Non-Krylov Subspace Method for Solving Large and Sparse Linear System of Equations.NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS,9(2),289-314.
MLA	Peng, Wujian,et al."A Non-Krylov Subspace Method for Solving Large and Sparse Linear System of Equations".NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS 9.2(2016):289-314.