A Minimum Residual Based Gradient Iterative Method for a Class of Matrix Equations

作     者：Qing-qing Zheng Qing-qing ZHENG

作者机构：Department of MathematicsCollege of ScienceChina University of Petroleum-BeijingBeijing102249China 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：2024年第40卷第1期

页      面：17-34页

核心收录：

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：supported by the National Natural Science Foundation of China (No. 12001311) Science Foundation of China University of Petroleum,Beijing (No. 2462021YJRC025) the State Key Laboratory of Petroleum Resources and Prospecting,China University of Petroleum 

主　　题：Sylvester matrix equation coupled matrix equation minimum residual gradient descent convergence analysis 

摘      要：In this paper, we present a minimum residual based gradient iterative method for solving a class of matrix equations including Sylvester matrix equations and general coupled matrix equations. The iterative method uses a negative gradient as steepest direction and seeks for an optimal step size to minimize the residual norm of next iterate. It is shown that the iterative sequence converges unconditionally to the exact solution for any initial guess and that the norm of the residual matrix and error matrix decrease monotonically. Numerical tests are presented to show the efficiency of the proposed method and confirm the theoretical results.