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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 Publication JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS ISSN 0377-0427 Volume 346Pages:490-504 Abstract This 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. Keyword Tensor-vector product Tensor equation Ellipsoid surface Alternating projection method Regularity DOI 10.1016/j.cam.2018.07.013 Language 英语 Funding Project National 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 Area Mathematics WOS Subject Mathematics, Applied WOS ID WOS:000449246500035 Publisher ELSEVIER SCIENCE BV Citation statistics Document Type 期刊论文 Identifier http://ir.amss.ac.cn/handle/2S8OKBNM/31749 Collection 计算数学与科学工程计算研究所 Corresponding Author Gao, Huan Affiliation 1.Cent S Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China2.Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Sci & Engn Comp, Beijing 100190, Peoples R China3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China4.Hunan First Normal Univ, Coll Math & Computat Sci, Changsha 410205, Hunan, Peoples R China Recommended CitationGB/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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