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An orthogonally accumulated projection method for symmetric linear system of equations
Peng WuJian1; Lin Qun2; Zhang ShuHua3
2016-07-01
Source PublicationSCIENCE CHINA-MATHEMATICS
ISSN1674-7283
Volume59Issue:7Pages:1235-1248
AbstractA 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.
Keyworditerative method accumulated projection conjugate gradient method Krylov subspace
DOI10.1007/s11425-016-5142-5
Language英语
Funding ProjectNational Natural Science Foundation of China[91430108] ; National Natural Science Foundation of China[11171251] ; Tianjin University of Finance and Economics[ZD1302]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000379083700001
PublisherSCIENCE PRESS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/23089
Collection计算数学与科学工程计算研究所
Corresponding AuthorZhang ShuHua
Affiliation1.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
Recommended Citation
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.
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