改进解决具有 $$\mathcal {M}$ - 张量的多线性系统的高斯-赛德尔迭代法

IF 0.7 4区数学 Q3 MATHEMATICS, APPLIED

Japan Journal of Industrial and Applied Mathematics Pub Date : 2023-12-14 DOI:10.1007/s13160-023-00637-z

Malihe Nobakht-Kooshkghazi, Mehdi Najafi-Kalyani

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引用次数: 0

摘要

本文的主要目的是利用基于张量分裂的预处理方法求解具有强（\mathcal {M}\）张量的多线性系统。本文提出了一种新的用于求解多线性系统的预条件高斯-赛德尔迭代法。本文讨论了所提方法的收敛性和比较定理。最后，我们给出了一些数值实验来证实我们的理论分析，并证明了所提方法的效率。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

$Improving the Gauss–Seidel iterative method for solving multi-linear systems with $$\mathcal {M}$$ -tensors$

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Improving the Gauss–Seidel iterative method for solving multi-linear systems with $$\mathcal {M}$$ -tensors

The main objective of this paper is to solve multi-linear systems with strong $ \mathcal {M}$-tensors using preconditioned methods based on tensor splitting. In this paper, we propose a new preconditioned Gauss–Seidel iterative method for solving multi-linear systems. The convergence and comparison theorems of the proposed method are discussed. Finally, some numerical experiments are given to confirm our theoretical analysis and demonstrate the efficiency of the proposed method.

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来源期刊

Japan Journal of Industrial and Applied Mathematics 数学-应用数学

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： Japan Journal of Industrial and Applied Mathematics (JJIAM) is intended to provide an international forum for the expression of new ideas, as well as a site for the presentation of original research in various fields of the mathematical sciences. Consequently the most welcome types of articles are those which provide new insights into and methods for mathematical structures of various phenomena in the natural, social and industrial sciences, those which link real-world phenomena and mathematics through modeling and analysis, and those which impact the development of the mathematical sciences. The scope of the journal covers applied mathematical analysis, computational techniques and industrial mathematics.