四元不定最小二乘问题的有效实结构保留算法

IF 1.7 3区数学 Q2 MATHEMATICS, APPLIED

Numerical Algorithms Pub Date : 2024-09-12 DOI:10.1007/s11075-024-01929-2

Zixiang Meng, Zhihan Zhou, Ying Li, Fengxia Zhang

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引用次数: 0

摘要

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。

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

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

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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来源期刊

Numerical Algorithms 数学-应用数学

CiteScore

4.00

自引率

9.50%

发文量

201

审稿时长

9 months

期刊介绍： The journal Numerical Algorithms is devoted to numerical algorithms. It publishes original and review papers on all the aspects of numerical algorithms: new algorithms, theoretical results, implementation, numerical stability, complexity, parallel computing, subroutines, and applications. Papers on computer algebra related to obtaining numerical results will also be considered. It is intended to publish only high quality papers containing material not published elsewhere.