交换四元数理论中总最小二乘问题的一种代数算法

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation Pub Date : 2025-01-09 DOI:10.1016/j.amc.2024.129268

Tongsong Jiang , Dong Zhang , Zhenwei Guo , V.I. Vasil'ev

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引用次数: 0

摘要

交换四元数总最小二乘（CQTLS）问题是求解矩阵A和B存在误差的超定线性方程组AX≈B的一种方法。在交换四元数理论的理论研究和数值计算中，CQTLS问题是研究电信、大地测量学和图像处理理论的一个非常有效的工具。本文利用可交换四元数矩阵的实表示，研究了CQTLS问题，导出了CQTLS问题具有可交换四元数解的充要条件，并给出了求解CQTLS问题的代数算法。

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An algebraic algorithm for the total least squares problem in commutative quaternionic theory

A commutative quaternion total least squares (CQTLS) problem is a method of solving overdetermined sets of linear equations

A X \approx B

with errors in the matrices A and B. In the theoretical studies and numerical calculations of commutative quaternionic theory, the CQTLS problem is an extremely effective tool for the study of telecommunications, geodesy, and image processing theory. This paper, by means of the real representation of a commutative quaternion matrix, studies the CQTLS problem, derives necessary and sufficient conditions for the CQTLS problem has a commutative quaternion solution, and gives an algebraic algorithm for solving the CQTLS problem.

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来源期刊

Applied Mathematics and Computation 数学-应用数学

CiteScore

7.90

自引率

10.00%

发文量

755

审稿时长

36 days

期刊介绍： Applied Mathematics and Computation addresses work at the interface between applied mathematics, numerical computation, and applications of systems – oriented ideas to the physical, biological, social, and behavioral sciences, and emphasizes papers of a computational nature focusing on new algorithms, their analysis and numerical results. In addition to presenting research papers, Applied Mathematics and Computation publishes review articles and single–topics issues.