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

被引：0
作者：
Qing-qing Zheng
机构：
[1] China University of Petroleum-Beijing,Department of Mathematics, College of Science
来源：
Acta Mathematicae Applicatae Sinica, English Series | 2024年 / 40卷
关键词：
Sylvester matrix equation; coupled matrix equation; minimum residual; gradient descent; convergence analysis; 15A06; 65F15; 15A24; 93B30;
D O I：
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学科分类号：
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.
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页码：17 / 34
页数：17
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