用于求解 $${mathcal {M}}$ 张量多线性系统的新型预处理高斯-赛德尔方法

IF 0.7 4区数学 Q3 MATHEMATICS, APPLIED Japan Journal of Industrial and Applied Mathematics Pub Date : 2024-08-23 DOI:10.1007/s13160-024-00670-6

Xuan-Le An, Xin-Mei Lv, Shu-Xin Miao

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引用次数: 0

摘要

通过利用与系数张量相关的大化矩阵每行的一些元素，我们提出了一种预处理方法，并给出了相应的预处理高斯-赛德尔方法，用于求解（{\mathcal {M}}\）张量多线性系统。从理论上，我们给出了所提出的预条件高斯-赛德尔方法的收敛性和比较定理。在数值上，我们通过一些例子证明了理论结果的正确性和所提预处理方法的高效性。

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A new preconditioned Gauss-Seidel method for solving $${\mathcal {M}}$$ -tensor multi-linear system

By utilizing some elements of each row of the majorization matrix associated with the coefficient tensor, we propose a preconditioner, and present the corresponding preconditioned Gauss–Seidel method for solving ${\mathcal {M}}$-tensor multi-linear system. Theoretically, we give the convergence and comparison theorems of the proposed preconditioned Gauss–Seidel method. Numerically, we show the correctness of theoretical results and the efficiency of the proposed preconditioner by some examples.

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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.