The GPBiCG(m, l) Method for Solving General Matrix Equations  

作　　者：Basem I. Selim Lei DU Bo YU Xuanru ZHU 

机构地区：[1]School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China [2]Mathematics and Computer Science Department, Faculty of Science, Menoufia University, Shebin El-Kom 32511, Egypt

出　　处：《Journal of Mathematical Research with Applications》2019年第4期408-432,共25页数学研究及应用（英文版）

基　　金：Supported by the National Natural Sciences Foundation of China(Grant Nos.11501079; 11571061);Part by the Higher Education Commission of Egypt

摘　　要：The generalized product bi-conjugate gradient(GPBiCG(m,l))method has been recently proposed as a hybrid variant of the GPBi CG and the Bi CGSTAB methods to solve the linear system Ax=b with non-symmetric coefficient matrix,and its attractive convergence behavior has been authenticated in many numerical experiments.By means of the Kronecker product and the vectorization operator,this paper aims to develop the GPBi CG(m,l)method to solve the general matrix equation■ and the general discrete-time periodic matrix equations■ which include the well-known Lyapunov,Stein,and Sylvester matrix equations that arise in a wide variety of applications in engineering,communications and scientific computations.The accuracy and efficiency of the extended GPBi CG(m,l)method assessed against some existing iterative methods are illustrated by several numerical experiments.The generalized product bi-conjugate gradient(GPBiCG(m,l))method has been recently proposed as a hybrid variant of the GPBi CG and the Bi CGSTAB methods to solve the linear system Ax=b with non-symmetric coefficient matrix,and its attractive convergence behavior has been authenticated in many numerical experiments.By means of the Kronecker product and the vectorization operator,this paper aims to develop the GPBi CG(m,l)method to solve the general matrix equation■and the general discrete-time periodic matrix equations■which include the well-known Lyapunov,Stein,and Sylvester matrix equations that arise in a wide variety of applications in engineering,communications and scientific computations.The accuracy and efficiency of the extended GPBi CG(m,l)method assessed against some existing iterative methods are illustrated by several numerical experiments.

关 键 词：GPBiCG(m l) METHOD Krylov SUBSPACE METHOD matrix EQUATIONS KRONECKER product VECTORIZATION operator 

分 类 号：O1[理学—数学]