对偶四元数厄密特征值问题的一种新的保结构方法

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2024-12-18 DOI:10.1016/j.aml.2024.109432

Wenxv Ding, Ying Li, Musheng Wei

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引用次数: 0

摘要

近年来，对偶四元数矩阵分解在编队控制和图像处理等领域发挥了重要作用。本文给出了对偶四元数厄米矩阵的特征值分解算法。该算法建立在对偶四元数厄米特矩阵对偶矩阵表示的保结构三对角化基础上，利用正交矩阵实现对偶矩阵的保结构三对角化。由于采用正交变换，该算法具有数值稳定性。通过数值实验验证了该算法的有效性。

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A new structure-preserving method for dual quaternion Hermitian eigenvalue problems

Dual quaternion matrix decompositions have played a crucial role in fields such as formation control and image processing in recent years. In this paper, we present an eigenvalue decomposition algorithm for dual quaternion Hermitian matrices. The proposed algorithm is founded on the structure-preserving tridiagonalization of the dual matrix representation of dual quaternion Hermitian matrices through the application of orthogonal matrices. Owing to the utilization of orthogonal transformations, the algorithm exhibits numerical stability. Numerical experiments are provided to illustrate the efficiency of the structure-preserving algorithm.

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来源期刊

Applied Mathematics Letters 数学-应用数学

CiteScore

7.70

自引率

5.40%

发文量

347

审稿时长

10 days

期刊介绍： The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.