修正共轭梯度算法求解四元数Sylvester张量方程  

Modified Conjugate Gradient Algorithm for Solving the Quaternion Sylvester Tensor Equation

作　　者：胡晶晶 柯艺芬 马昌凤[1,2,3] HU Jingjing;KE Yifen;MA Changfeng(School of Mathematics and Statistics,Fujian Normal University,Fuzhou 350117,China;Key Laboratory of Analytical Mathematical and Applications(Ministry of Education),Fujian Normal University,Fuzhou 350117,China;Center for Applied Mathematics of Fujian province(FJNU),Fuzhou 350117,China)

机构地区：[1]福建师范大学数学与统计学院,福建福州350117 [2]福建师范大学分析数学及应用教育部重点实验室,福建福州350117 [3]福建省应用数学中心,福建福州350117

出　　处：《应用数学》2024年第1期238-250,共13页Mathematica Applicata

基　　金：国家自然科学基金资助项目(12371378,11901098);福建省自然科学基金(2023J011127,2020J05034)。

摘　　要：本文提出一类张量形式的修正共轭梯度算法求解四元数Sylvester张量方程.证明在不计舍入误差的情况下,所提方法可在有限迭代步内获得张量方程组的解.进一步,通过选择特殊类型的初始张量,可获得方程组的唯一极小Frobenius范数解.通过数值算例验证了所提出算法的可行性和有效性.This paper presents a class of tensor form modified conjugate gradient algorithm for solving the quaternion Sylvester tensor equation.It is proved that the proposed algorithm can obtain the solution of the tensor equation with in a finite number of iteration steps in the absence of round-off errors.Furthermore,we can get the unique minimal Frobenius norm solution by choosing a special type of initial tensor.Numerical examples demonstrate the feasibility and effectiveness of the proposed algorithm.

关 键 词：四元数 Sylvester张量方程 修正共轭梯度算法 

分 类 号：O241.6[理学—计算数学]