Alternating projection method for a class of tensor equations

doi:10.1016/j.cam.2018.07.013

	Alternating projection method for a class of tensor equations
	Li, Zhibao 1; Dai, Yu-Hong2,3 ; Gao, Huan 4
	2019-01-15
发表期刊	JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
ISSN	0377-0427
卷号	346 页码:490-504
摘要	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.
关键词	Tensor-vector product Tensor equation Ellipsoid surface Alternating projection method Regularity
DOI	10.1016/j.cam.2018.07.013
语种	英语
资助项目	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研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000449246500035
出版者	ELSEVIER SCIENCE BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/31749
专题	计算数学与科学工程计算研究所
通讯作者	Gao, Huan
作者单位	1.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
推荐引用方式 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.