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

doi:10.4208/nmtma.2016.y14014

	A Non-Krylov Subspace Method for Solving Large and Sparse Linear System of Equations
	Peng, Wujian 1; Lin, Qun2
	2016-05-01
发表期刊	NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS
ISSN	1004-8979
卷号	9 期号:2 页码:289-314
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.
关键词	Iterative method accumulated projection Krylov subspace
DOI	10.4208/nmtma.2016.y14014
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000377119800007
出版者	CAMBRIDGE UNIV PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/22844
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.