Research On Precondition Iteration Method For Coupled Sylvester Matrix Equations

The coupled Sylvester matrix equations arise in numerous applied areas such as scientific computing and engineering applications,numerical solution problem also play an important role in linear control and image restoration and other problems.In this paper,we focus on numerical solution of the coupled Sylvester matrix equations.It is well known that the convergence rate of the Krylov subspace methods is rel atively slow in many cases, for accelerating the rate of convergence of global FOM a nd global GMRES.This paper presents a preconditioned version of global FOM and gl obal GMRES for solving coupled Sylvester matrix equations:AX1+X2B=C and DX1+X2 E=C.As follows:First,using Gauss-Seidel preconditioning,we transform the original coupl ed Sylvester matrix equations to another equation.We then apply the global Arnoldi method and get low rank approximate solutions.Finally,some theoretical results are give n. As numerical results show, it is essential to use preconditioning in association with Krylov subspace methods.