Global FOM and GMRES algorithms for matrix equations

In the present paper, we present new methods for solving nonsymmetric linea r systems of equations with multiple right-hand sides. These methods are ba sed on global oblique and orthogonal projections of the initial matrix resi dual onto a matrix Krylov subspace. We first derive the global full orthogo nalization method and give its properties. The second method which is a glo bal orthogonal projection method is the global generalized minimum residual method. We then give some properties of this new algorithm. We also show h ow to apply these methods for solving the Lyapunov matrix equation. Finally , numerical examples will be given. (C) 1999 Elsevier Science B.V. and IMAC S. All rights reserved.