An efficient method for the split quaternion equality constrained least squares problem in split quaternionic mechanics

被引：1

作者：

Wang, Gang ^{[1
]}

Jiang, Tongsong ^{[2
,3
]}

Zhang, Dong ^{[1
]}

Vasil'ev, V. I. ^{[1
]}

机构：

[1] North Eastern Fed Univ, Inst Math & Informat Sci, Yakutsk 677000, Russia

[2] Shandong Xiandai Univ, Sch Elect Informat, Jinan 250104, Shandong, Peoples R China

[3] Linyi Univ, Sch Math & Stat, Linyi 276005, Shandong, Peoples R China

来源：

COMPUTATIONAL & APPLIED MATHEMATICS | 2023年 / 42卷 / 06期

基金：

俄罗斯科学基金会;

关键词：

Split quaternion matrix; Real representation matrix; Generalized singular value decomposition; LSESQ problem; Split quaternionic mechanics; ALGEBRAIC TECHNIQUES; EIGENVECTORS; EIGENVALUES; DYNAMICS; MATRIX;

D O I：

10.1007/s40314-023-02377-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the theoretical explorations and numerical computations of split quaternionic mechanics, a common and extremely effective tool for the study of quantum mechanics and quantum field theory is the split quaternion equality constrained least squares (LSESQ) problem. This paper for the first time studies the generalized singular value decomposition of split quaternion matrices (GSVDSQ) based on the 2x2 isomorphic representation of split quaternion matrices and obtains a GSVDSQ theorem. In addition, this paper proves the necessary and sufficient conditions for the LSESQ problem to have solutions and gives an efficient method for solving the LSESQ problem. Finally, two numerical examples are presented to demonstrate the efficiency of the proposed method.

引用

页数：13

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