An orthogonally accumulated projection method for symmetric linear system of equations

doi:10.1007/s11425-016-5142-5

	An orthogonally accumulated projection method for symmetric linear system of equations
	Peng WuJian 1; Lin Qun2 ; Zhang ShuHua 3
	2016-07-01
发表期刊	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
卷号	59 期号:7 页码:1235-1248
摘要	A direct as well as iterative method (called the orthogonally accumulated projection method, or the OAP for short) for solving linear system of equations with symmetric coefficient matrix is introduced in this paper. With the Lanczos process the OAP creates a sequence of mutually orthogonal vectors, on the basis of which the projections of the unknown vectors are easily obtained, and thus the approximations to the unknown vectors can be simply constructed by a combination of these projections. This method is an application of the accumulated projection technique proposed recently by the authors of this paper, and can be regarded as a match of conjugate gradient method (CG) in its nature since both the CG and the OAP can be regarded as iterative methods, too. Unlike the CG method which can be only used to solve linear systems with symmetric positive definite coefficient matrices, the OAP can be used to handle systems with indefinite symmetric matrices. Unlike classical Krylov subspace methods which usually ignore the issue of loss of orthogonality, OAP uses an effective approach to detect the loss of orthogonality and a restart strategy is used to handle the loss of orthogonality. Numerical experiments are presented to demonstrate the efficiency of the OAP.
关键词	iterative method accumulated projection conjugate gradient method Krylov subspace
DOI	10.1007/s11425-016-5142-5
语种	英语
资助项目	National Natural Science Foundation of China[91430108] ; National Natural Science Foundation of China[11171251] ; Tianjin University of Finance and Economics[ZD1302]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000379083700001
出版者	SCIENCE 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/23089
专题	计算数学与科学工程计算研究所
通讯作者	Zhang ShuHua
作者单位	1.Zhaoqing Univ, Dept Math & Stat, Zhaoqing 526061, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.Tianjin Univ Finance & Econ, Res Ctr Math & Econ, Tianjin 300204, Peoples R China
推荐引用方式 GB/T 7714	Peng WuJian,Lin Qun,Zhang ShuHua. An orthogonally accumulated projection method for symmetric linear system of equations[J]. SCIENCE CHINA-MATHEMATICS,2016,59(7):1235-1248.
APA	Peng WuJian,Lin Qun,&Zhang ShuHua.(2016).An orthogonally accumulated projection method for symmetric linear system of equations.SCIENCE CHINA-MATHEMATICS,59(7),1235-1248.
MLA	Peng WuJian,et al."An orthogonally accumulated projection method for symmetric linear system of equations".SCIENCE CHINA-MATHEMATICS 59.7(2016):1235-1248.