求解Sylvester方程AXB+CX=D的OROD方法的几个性质

数学理论与应用 ›› 2016, Vol. 36 ›› Issue (4): 50-56.

求解Sylvester方程AXB+CX=D的OROD方法的几个性质

邓建平

长沙理工大学数学与统计学院,长沙,410004

出版日期:2016-12-30 发布日期:2020-09-25
基金资助:
湖南省自然科学基金项目(14JJ3084);

湖南省教育厅科学研究项目(13B137)

Several Properties of the OROD Method for Solving the Sylvester Equation AXB+CX=D

Deng Jianping

School of Mathematics and Statistics,Changsha University of Science and Technology,Changsha 410014,China

Online:2016-12-30 Published:2020-09-25

摘要/Abstract

摘要： 本文讨论了求解Sylvester方程AXB+CX=D的OROD迭代法(正交残量法和正交方向迭代法)的几个重要性质,证明了该算法产生的误差序列是单调递减的,同时给出了该算法的最小化性质的精确刻画,最后给出了一些数值例子.

关键词: 广义共轭梯度法, Sylvester方程, 收敛

Abstract: This paper presents several properties of the OROD iterative method(orthogonal residual method and the orthogonal direction method)for solving the Sylvester equation AXB+CX= D.It is showed that the corresponding error sequence decreases monotonely.The minimization property of the method is precisely characterized.A numerical example is presented in the end.

Key words: Generalized conjugate gradient method, Sylvester equation, Convergence

邓建平. 求解Sylvester方程AXB+CX=D的OROD方法的几个性质[J]. 数学理论与应用, 2016, 36(4): 50-56.

Deng Jianping.

Several Properties of the OROD Method for Solving the Sylvester Equation AXB+CX=D [J]. Mathematical Theory and Applications, 2016, 36(4): 50-56.