The BiCG Algorithm for Solving the Minimal Frobenius Norm Solution of Generalized Sylvester Tensor Equation over the Quaternions

被引：4
作者：
Xie, Mengyan [1 ,2 ,3 ]
Wang, Qing-Wen [2 ,3 ,4 ]
Zhang, Yang [5 ]
机构：
[1] Shanghai Ocean Univ, Coll Informat Technol, Shanghai 201306, Peoples R China
[2] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China
[3] Shanghai Univ, Newtouch Ctr Math, Shanghai 200444, Peoples R China
[4] Collaborat Innovat Ctr Marine Artificial Intellige, Shanghai 200444, Peoples R China
[5] Univ Manitoba, Dept Math, Winnipeg, MB R3T 2N2, Canada
来源：
SYMMETRY-BASEL | 2024年 / 16卷 / 09期
基金：
加拿大自然科学与工程研究理事会;
关键词：
quaternion tensor; sylvester tensor equation; iterative algorithm; color video restoration; LEAST-SQUARES SOLUTIONS; ITERATIVE ALGORITHM; MATRIX EQUATIONS; APPROXIMATION; SYSTEM; COMPUTATION; AXB;
D O I：
10.3390/sym16091167
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
In this paper, we develop an effective iterative algorithm to solve a generalized Sylvester tensor equation over quaternions which includes several well-studied matrix/tensor equations as special cases. We discuss the convergence of this algorithm within a finite number of iterations, assuming negligible round-off errors for any initial tensor. Moreover, we demonstrate the unique minimal Frobenius norm solution achievable by selecting specific types of initial tensors. Additionally, numerical examples are presented to illustrate the practicality and validity of our proposed algorithm. These examples include demonstrating the algorithm's effectiveness in addressing three-dimensional microscopic heat transport and color video restoration problems.
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页数：22
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