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

被引：8
|
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
收藏
页数：12
相关论文
共 50 条
  • [1] QUATERNION GENERALIZED SINGULAR VALUE DECOMPOSITION AND ITS APPLICATIONS
    Jiang Tongsong1 Liu Yonghui2 Wei Musheng21 Dept. of Math.
    Dept. of Comput. Sci. and Tech.
    Applied Mathematics A Journal of Chinese Universities(Series B), 2006, (01) : 113 - 118
  • [2] Quaternion generalized singular value decomposition and its applications
    Jiang T.
    Liu Y.
    Wei M.
    Applied Mathematics-A Journal of Chinese Universities, 2006, 21 (1) : 113 - 118
  • [3] Quaternion matrix singular value decomposition and its applications for color image processing
    Pei, SC
    Chang, JH
    Ding, JJ
    2003 INTERNATIONAL CONFERENCE ON IMAGE PROCESSING, VOL 1, PROCEEDINGS, 2003, : 805 - 808
  • [4] Jacobi method for quaternion matrix singular value decomposition
    Le Bihan, Nicolas
    Sangwine, Stephen J.
    APPLIED MATHEMATICS AND COMPUTATION, 2007, 187 (02) : 1265 - 1271
  • [5] Denoising color images by reduced quaternion matrix singular value decomposition
    Shan Gai
    Guowei Yang
    Minghua Wan
    Lei Wang
    Multidimensional Systems and Signal Processing, 2015, 26 : 307 - 320
  • [6] Denoising color images by reduced quaternion matrix singular value decomposition
    Gai, Shan
    Yang, Guowei
    Wan, Minghua
    Wang, Lei
    MULTIDIMENSIONAL SYSTEMS AND SIGNAL PROCESSING, 2015, 26 (01) : 307 - 320
  • [7] A complex structure-preserving algorithm for computing the singular value decomposition of a quaternion matrix and its applications
    Zhang, Dong
    Jiang, Tongsong
    Jiang, Chuan
    Wang, Gang
    NUMERICAL ALGORITHMS, 2024, 95 (01) : 267 - 283
  • [8] A complex structure-preserving algorithm for computing the singular value decomposition of a quaternion matrix and its applications
    Dong Zhang
    Tongsong Jiang
    Chuan Jiang
    Gang Wang
    Numerical Algorithms, 2024, 95 : 267 - 283
  • [9] Incremental quaternion singular value decomposition and its application for low rank quaternion matrix completion
    Xu, Yang
    Gao, Kaixin
    COMPUTATIONAL & APPLIED MATHEMATICS, 2024, 43 (06):
  • [10] Generalized essential matrix: Properties of the singular value decomposition
    Miraldo, Pedro
    Araujo, Helder
    IMAGE AND VISION COMPUTING, 2015, 34 : 45 - 50
12345