The Iterative Projection Methods For Large Stein Matrix Equations

This paper mainly studies iterative projection methods for solving large Stein matrix equation, andproposes three iterative projection methods. We promote the global-GMRES method and global-GMERR method for solving matrix equation AX B, and proposes the generalized global-GMRESmethod and generalized global-GMERR method for solving Stein matrix equations, respectively. Inorder to solve the dense Stein matrix equation, we propose the block Arnoldi-Stein method, based onthe block Arnoldi method. We also promote the global-GMRES method and global-GMERR method,and popose the generalized global-GMRES method and generalized global-GMERR method forsolving general linear matrix equations, respectively.In the paper, the convergence of the generalized global-GMRES method and generalized global-GMERR method are proved, respectively. The error upper bound of the approximate solution is given,which is obtained by the block Arnoldi-Stein method for solving Stein matrix equation. Numericalexperiments also show the effectiveness of the proposed methods.