Global FOM and GMRES algorithms for a class of complex matrix equations

In this paper, a generalized global Arnoldi process is given to produce an F-orthonormal basis of complex matrix space. Then we propose the global full orthogonalization method (Gl-FOM) and global generalized minimum residual (Gl-GMRES) method for solving a class of complex matrix equations. The new methods can be implemented by the original coefficient matrices. By using Schur complement, we give the expressions of the approximate solutions and the corresponding residuals. Some convergence results of the proposed methods are also derived. Finally, numerical examples are given to illustrate the effectiveness with comparison to other existing methods.