anorthogonallyaccumulatedprojectionmethodforsymmetriclinearsystemofequations

	anorthogonallyaccumulatedprojectionmethodforsymmetriclinearsystemofequations
	Peng Wujian 1; Lin Qun2 ; Zhang Shuhua 3
	2016
发表期刊	sciencechinamathematics
ISSN	1674-7283
卷号	59 期号:7 页码:1235
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.
语种	英语
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/44043
专题	计算数学与科学工程计算研究所
作者单位	1.肇庆学院 2.中国科学院数学与系统科学研究院 3.天津财经大学
推荐引用方式 GB/T 7714	Peng Wujian,Lin Qun,Zhang Shuhua. anorthogonallyaccumulatedprojectionmethodforsymmetriclinearsystemofequations[J]. sciencechinamathematics,2016,59(7):1235.
APA	Peng Wujian,Lin Qun,&Zhang Shuhua.(2016).anorthogonallyaccumulatedprojectionmethodforsymmetriclinearsystemofequations.sciencechinamathematics,59(7),1235.
MLA	Peng Wujian,et al."anorthogonallyaccumulatedprojectionmethodforsymmetriclinearsystemofequations".sciencechinamathematics 59.7(2016):1235.