Solving the system of nonsingular tensor equations via randomized Kaczmarz-like method

A great deal of attention has been paid to solve the system of tensor equations in recent years for its applications in various fields. In this paper, the Kaczmarz-like method, which is an effective approach for solving linear equations, is considered to deal with the system of tensor equations with...

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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 421; p. 114856
Main Authors: Wang, Xuezhong, Che, Maolin, Mo, Changxin, Wei, Yimin
Format: Journal Article
Language:English
Published: Elsevier B.V 15.03.2023
Subjects:
Convergence analysis
Convergence rate
Kaczmarz method
Randomized algorithm
The system of tensor equations
65C20
Kaczmarz method
Convergence rate
15A69
Randomized algorithm
65J15
The system of tensor equations
Convergence analysis
ISSN:0377-0427, 1879-1778
Online Access:Get full text
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Summary:A great deal of attention has been paid to solve the system of tensor equations in recent years for its applications in various fields. In this paper, the Kaczmarz-like method, which is an effective approach for solving linear equations, is considered to deal with the system of tensor equations with nonsingular coefficient tensors. To reach this goal, two algorithms, i.e., the randomized Kaczmarz-like algorithm and its relaxed version, are proposed. The convergence analysis of these two approaches are given based on matrix SVD and the local tangential cone condition. Moreover, we present estimations of the convergence rate. Several numerical examples are presented to validate the theoretical results and reliability as well as effectiveness.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2022.114856