Invertible matrices under non-Archimedean absolute value and its inverse

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2025-04-19 DOI:10.1016/j.cam.2025.116700

Suhua Li, Chaoqian Li

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引用次数: 0

Abstract

Invertible matrices play a crucial role in various areas of mathematics, science and engineering. Although there are many ways to determine whether a matrix is invertible or not, it is still a fundamental and an important research work in linear algebra, especially in large-scale numerical computations. Based on the non-Archimedean absolute value, we in this paper present a new class of invertible matrices called doubly strictly diagonally dominant matrices under non-Archimedean absolute value (DSDD

_{n . A .}

matrices). It includes the strictly diagonally dominant matrices under non-Archimedean absolute value (SDD

_{n . A .}

matrices) presented by Nica and Sprague in [The American Mathematical Monthly, 130 (2023) 267-275]. Some examples are given to show the relationships of SDD

_{n . A .}

matrices, DSDD

_{n . A .}

matrices, SDD matrices (strictly diagonally dominant matrices under Archimedean absolute value), DSDD matrices (doubly strictly diagonally dominant matrices under Archimedean absolute value), and H-matrices. Moreover, it is proved that the inverse of DSDD

_{n . A .}

matrices is also DSDD

_{n . A .}

in some cases, which displays remarkable difference with the inverse of DSDD matrices and SDD matrices.

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非阿基米德绝对值下的可逆矩阵及其逆

可逆矩阵在数学、科学和工程的各个领域起着至关重要的作用。虽然确定矩阵是否可逆的方法有很多，但它仍然是线性代数，特别是大规模数值计算中的一项基础和重要的研究工作。本文在非阿基米德绝对值的基础上，提出了一类新的可逆矩阵，称为非阿基米德绝对值下的双严格对角占优矩阵。矩阵)。它包括非阿基米德绝对值（sddna . a）下的严格对角占优矩阵。矩阵)由Nica和Sprague在[The American Mathematical Monthly， 130(2023) 267-275]中提出。举例说明了sddna与a的关系。矩阵,DSDDn.A。矩阵、SDD矩阵（阿基米德绝对值下严格对角占优矩阵）、DSDD矩阵（阿基米德绝对值下双严格对角占优矩阵）和h矩阵。此外，还证明了dsddna . a的逆序列。矩阵也是dddna。在某些情况下，它与DSDD矩阵和SDD矩阵的逆表现出显著的差异。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.