On singular value decomposition and generalized inverse of a commutative quaternion matrix and applications

被引：10

作者：

Zhang, Dong ^{[1
]}

Jiang, Tongsong ^{[2
,3
]}

Wang, Gang ^{[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：

APPLIED MATHEMATICS AND COMPUTATION | 2024年 / 460卷

基金：

俄罗斯科学基金会;

关键词：

Commutative quaternion matrix; Complex representation; Moore-Penrose generalized inverse; Singular value decomposition; Least squares problem; STRUCTURE-PRESERVING METHOD;

D O I：

10.1016/j.amc.2023.128291

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

By means of a complex representation of a commutative quaternion matrix, the singular value decomposition and the generalized inverse problems of a commutative quaternion matrix are studied, and the corresponding theorems and algorithms are given. In addition, based on the singular value decomposition and generalized inverse of a commutative quaternion matrix, the numerical experiments for solving the least squares problem and the color image watermarking problem are given. Numerical experiments illustrate the effectiveness and reliability of the proposed algorithms.

引用

页数：12

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