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Alternating projection method for a class of tensor equations
Li, Zhibao1; Dai, Yu-Hong2,3; Gao, Huan4
2019-01-15
Source PublicationJOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
ISSN0377-0427
Volume346Pages:490-504
AbstractThis paper considers how to solve a class of tensor equations arising from the unified definition of tensor vector products. Of special interest is the order-3 tensor equation whose solutions are the intersection of a group of quadrics from a geometric point of view. Inspired by the method of alternating projections for set intersection problems, we develop a hybrid alternating projection algorithm for solving order-3 tensor equations. The local linear convergence of the alternating projection method is established under suitable conditions. Some numerical experiments are conducted to evaluate the effect of the proposed algorithm. (C) 2018 Elsevier B.V. All rights reserved.
KeywordTensor-vector product Tensor equation Ellipsoid surface Alternating projection method Regularity
DOI10.1016/j.cam.2018.07.013
Language英语
Funding ProjectNational Natural Science Foundation of China[11631013] ; National Natural Science Foundation of China[71331001] ; National Natural Science Foundation of China[11331012] ; National Natural Science Foundation of China[11701575] ; National 973 Program of China[2015CB856002] ; Natural Science Foundation of Hunan Province of China[2018E3624] ; Natural Science Foundation of Hunan Province of China[2018JJ3093]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000449246500035
PublisherELSEVIER SCIENCE BV
Citation statistics
Cited Times:1[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/31749
Collection计算数学与科学工程计算研究所
Affiliation1.Cent S Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Sci & Engn Comp, Beijing 100190, Peoples R China
3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
4.Hunan First Normal Univ, Coll Math & Computat Sci, Changsha 410205, Hunan, Peoples R China
Recommended Citation
GB/T 7714
Li, Zhibao,Dai, Yu-Hong,Gao, Huan. Alternating projection method for a class of tensor equations[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,2019,346:490-504.
APA Li, Zhibao,Dai, Yu-Hong,&Gao, Huan.(2019).Alternating projection method for a class of tensor equations.JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,346,490-504.
MLA Li, Zhibao,et al."Alternating projection method for a class of tensor equations".JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 346(2019):490-504.
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