CONVERGENCE RESULTS OF THE BICONJUGATE RESIDUAL ALGORITHM FOR SOLVING GENERALIZED SYLVESTER MATRIX EQUATION

作     者：Hajarian, Masoud 

作者机构：Shahid Beheshti Univ Fac Math Sci Dept Math Gen Campus Tehran 19839 Iran 

出 版 物：《ASIAN JOURNAL OF CONTROL》 (亚洲控制杂志)

年 卷 期：2017年第19卷第3期

页      面：961-968页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 08[工学] 0811[工学-控制科学与工程] 

主　　题：Biconjugate residual algorithm finite number of iterations generalized Sylvester matrix equation 

摘      要：In this article, we investigate a variant of the biconjugate residual (BCR) algorithm to solve the generalized Sylvester matrix equation Sigma(k)(i=1) A(i)XB(i) + Sigma(l)(j=1) CjYDj = E , which includes the well-known Lyapunov, Stein and Sylvester matrix equations. We show that the BCR algorithm with any (special) initial matrix pair can smoothly compute the (least Frobenius norm) solution pair of the generalized Sylvester matrix equation within a finite number of iterations in the absence of round-off errors. Finally the accuracy and effectiveness of the BCR algorithm in comparison to some existing algorithms are demonstrated by two numerical examples.