解一般矩阵方程的GPBiCG(m,l)法

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.