Perturbation analysis of matrices over a quaternion division algebra

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Electronic Transactions on Numerical Analysis Pub Date : 2021-01-01 DOI:10.1553/ETNA_VOL54S128

Sk. Safique Ahmad, I. Ali, I. Slapničar

引用次数: 1

Abstract

In this paper, we present the concept of perturbation bounds for the right eigenvalues of a quaternionic matrix. In particular, a Bauer-Fike-type theorem for the right eigenvalues of a diagonalizable quaternionic matrix is derived. In addition, perturbations of a quaternionic matrix are discussed via a block-diagonal decomposition and the Jordan canonical form of a quaternionic matrix. The location of the standard right eigenvalues of a quaternionic matrix and a sufficient condition for the stability of a perturbed quaternionic matrix are given. As an application, perturbation bounds for the zeros of quaternionic polynomials are derived. Finally, we give numerical examples to illustrate our results.

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四元数除法代数上矩阵的微扰分析

本文给出了四元数矩阵右特征值的摄动界的概念。特别地，导出了可对角四元数矩阵右特征值的一个bauer - fike型定理。此外，通过块对角分解和四元数矩阵的约当标准形式讨论了四元数矩阵的微扰。给出了四元数矩阵标准右特征值的位置和摄动四元数矩阵稳定性的充分条件。作为应用，导出了四元数多项式零点的摄动界。最后，给出了数值算例来说明我们的结果。

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

Electronic Transactions on Numerical Analysis 数学-应用数学

CiteScore

2.10

自引率

7.70%

发文量

审稿时长

6 months

期刊介绍： Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM).