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Study on semi-conjugate direction methods for non-symmetric systems
Dai, YH; Yuan, JY
2004-06-28
Source PublicationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
ISSN0029-5981
Volume60Issue:8Pages:1383-1399
AbstractSome theoretical problems and implementation problems are studied here for the semi-conjugate direction method established by Yuan, Golub, Plemmons and Cecilio (2002). The existence of semi-conjugate directions is proved for almost all matrices except skew-symmetric matrices. A new technique is proposed to overcome the breakdown problem appeared in the semi-conjugate direction method. In the implementation of the semi-conjugate direction method, the generation of the semi-conjugate direction is very important and necessary, but very expensive. The technique of limited-memory is introduced to economize the cost of the generation of the semi-conjugate direction in the Yuan-Golub-Plemmons-Cecilio algorithm. Finally, some numerical experiments are given to confirm our theoretical results. Our results illustrate that the semi-conjugate direction method is very nice alternative for solving non-symmetric systems, and the limited-memory left conjugate direction method is a good improvement of the left conjugate direction method. Copyright (C) 2004 John Wiley Sons, Ltd.
Keywordnon-singular matrix linear system semi-conjugate direction left conjugate direction left conjugate direction method left conjugate direction method existence breakdown limited-memory left conjugate direction method conjugate gradient method
DOI10.1002/nme.983
Language英语
WOS Research AreaEngineering ; Mathematics
WOS SubjectEngineering, Multidisciplinary ; Mathematics, Interdisciplinary Applications
WOS IDWOS:000222323200004
PublisherJOHN WILEY & SONS LTD
Citation statistics
Cited Times:6[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/19281
Collection计算数学与科学工程计算研究所
Affiliation1.Univ Fed Parana, Dept Matemat, Ctr Politecn, BR-81531990 Curitiba, Parana, Brazil
2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci & Engn Comp, Beijing 100080, Peoples R China
Recommended Citation
GB/T 7714
Dai, YH,Yuan, JY. Study on semi-conjugate direction methods for non-symmetric systems[J]. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING,2004,60(8):1383-1399.
APA Dai, YH,&Yuan, JY.(2004).Study on semi-conjugate direction methods for non-symmetric systems.INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING,60(8),1383-1399.
MLA Dai, YH,et al."Study on semi-conjugate direction methods for non-symmetric systems".INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 60.8(2004):1383-1399.
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