A note on the preconditioned tensor splitting iterative method for solving strong $ \mathcal{M} $-tensor systems-Reference-Cited by-同舟云学术

A note on the preconditioned tensor splitting iterative method for solving strong $ \mathcal{M} $-tensor systems

Published:2022 Issue:4 Volume:7 Page:7177-7186
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Liu Qingbing, ,Xu Aimin,Yin Shuhua,Tu Zhe

Abstract

<abstract><p>In this note, we present a new preconditioner for solving the multi-linear systems, which arise from many practical problems and are different from the traditional linear systems. Based on the analysis of the spectral radius, we give new comparison results between some preconditioned tensor splitting iterative methods. Numerical examples are given to demonstrate the efficiency of the proposed preconditioned method.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference16 articles.

1. L. Qi, Eigenvalues of a real supersymmetric tensor, J. Symb. Comput., 40 (2005), 1302–1324. https://doi.org/10.1016/j.jsc.2005.05.007

2. K. Pearson, Essentially positive tensors, Int. J. Algebra., 4 (2010), 421–427.

3. D. Liu, W. Li, S. Vong, The tensor splitting with application to solve multi-linear systems, J. Comput. Appl. Math., 330 (2018), 75–94. https://doi.org/10.1016/j.cam.2017.08.009

4. W. Li, D. Liu, S. Vong, Comparison results for splitting iterations for solving multi-linear system, Appl. Numer. Math., 134 (2018), 105–121. https://doi.org/10.1016/j.apnum.2018.07.009

5. L. Cui, M. Li, Y. Song, Preconditioned tensor splitting iterations method for solving multi-linear systems, Appl. Math. Lett., 96 (2019), 89–94. https://doi.org/10.1016/j.aml.2019.04.019

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. A new preconditioned AOR-type method for M-tensor equation;Applied Numerical Mathematics;2023-07