Alternating projection method for a class of tensor equations

被引：23
|
作者：
Li, Zhibao [1 ]
Dai, Yu-Hong [2 ,3 ]
Gao, Huan [4 ]
机构：
[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
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2019年 / 346卷
基金：
中国国家自然科学基金;
关键词：
Tensor-vector product; Tensor equation; Ellipsoid surface; Alternating projection method; Regularity; SOLVING MULTILINEAR SYSTEMS; FAST ALGORITHMS; PRODUCT; DECOMPOSITIONS; CONVERGENCE; EIGENVALUES; NOTATION;
D O I：
10.1016/j.cam.2018.07.013
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
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.
引用
收藏
页码：490 / 504
页数：15
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