The scaling conjugate gradient iterative method for two types of linear matrix equations

Abstract

In this paper, we propose a new iteration method which is based on the conjugate gradient method for solving the linear matrix equations of the form AiXBi=Fi,(i=1,2,…,N) and the generalized Sylvester matrix equation AXB+CXD=E. This method is compared with some existing methods in detail, such as gradient based iterative (GI) method and least squares iterative (LSI) method (Ding et al. 2010) proposed by Ding et al., also cyclic and simultaneous methods (Tang et al. 2014) given by Tang et al. Some numerical experiments demonstrate that the introduced iterative method is more efficient than the four existing methods.