Extending GCR Algorithm for the Least Squares Solutions on a Class of Sylvester Matrix Equations  

作　　者：Baohua Huang Changfeng Ma 

机构地区：[1]College of Mathematics and Informatics,Fujian Key Laborotary of Mathematical Analysis and Applications,Fujian Normal University,Fuzhou 350117,China

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2018年第1期140-159,共20页高等学校计算数学学报（英文版）

基　　金：Supported by Fujian Natural ScienceFoundation(Grant No.2016J01005);Strategic Priority Research Program of the Chinese Academy of Sciences(Grant No.XDB18010202).

摘　　要：The purpose of this paper is to derive the generalized conjugate residual(GCR)algorithm for finding the least squares solution on a class of Sylvester matrix equations.We prove that if the system is inconsistent,the least squares solution can be obtained within finite iterative steps in the absence of round-off errors.Furthermore,we provide a method for choosing the initial matrix to obtain the minimum norm least squares solution of the problem.Finally,we give some numerical examples to illustrate the performance of GCR algorithm.

关 键 词：Sylvester matrix equation Least squares solution Generalized conjugate residual algorithm Numerical experiments 

分 类 号：O17[理学—数学]