An effective real structure-preserving algorithm for the quaternion indefinite least squares problem

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-09-12 DOI:10.1007/s11075-024-01929-2

Zixiang Meng, Zhihan Zhou, Ying Li, Fengxia Zhang

引用次数: 0

Abstract

This paper concentrates on the quaternion indefinite least squares (QILS) problem. Firstly, we define the quaternion J-unitary matrix and the quaternion hyperbolic Givens rotation, and study their properties. Then, based on these, we investigate the quaternion hyperbolic QR factorization, and purpose its real structure-preserving (SP) algorithm by the real representation (Q-RR) matrix of the quaternion matrix. Immediately after, we explore the solution of the QILS problem, and give a real SP algorithm of solving the QILS problem. Eventually, to illustrate the effectiveness of proposed algorithms, we offer numerical examples.

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四元不定最小二乘问题的有效实结构保留算法

本文主要研究四元数不定最小二乘（QILS）问题。首先，我们定义了四元数 J 单位矩阵和四元数双曲 Givens 旋转，并研究了它们的性质。在此基础上，我们研究了四元双曲 QR 因式分解，并通过四元矩阵的实表示（Q-RR）矩阵实现了其实结构保留（SP）算法。紧接着，我们探讨了 QILS 问题的求解，并给出了求解 QILS 问题的实 SP 算法。最后，为了说明所提算法的有效性，我们提供了数值示例。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

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