Krylov subspace methods to solve a class of tensor equations via the Einstein product

被引：28
|
作者：
Huang, Baohua [1 ,2 ]
Xie, Yajun [3 ]
Ma, Changfeng [1 ,2 ]
机构：
[1] Fujian Normal Univ, Coll Math & Informat, Fuzhou 350117, Fujian, Peoples R China
[2] Fujian Normal Univ, FJKLMAA, Fuzhou 350117, Fujian, Peoples R China
[3] Fujian Jiangxia Univ, Sch Math & Phys, Fuzhou, Fujian, Peoples R China
来源：
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS | 2019年 / 26卷 / 04期
关键词：
Einstein product; global GMRES method; MINIRES method; SYMMLQ method; tensor equations; CRITERIA; SYSTEMS;
D O I：
10.1002/nla.2254
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper is concerned with some of the well-known iterative methods in their tensor forms to solve a class of tensor equations via the Einstein product. More precisely, the tensor forms of the Arnoldi and Lanczos processes are derived and the tensor form of the global GMRES method is presented. Meanwhile, the tensor forms of the MINIRES and SYMMLQ methods are also established. The proposed methods use tensor computations with no matricizations involved. Numerical examples are provided to illustrate the efficiency of the proposed methods and testify the conclusions suggested in this paper.
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收藏
页数：22
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