Global FOM and GMRES algorithms for matrix equations Original Research Article

In the present paper, we present new methods for solving nonsymmetric linear systems of equations with multiple right-hand sides. These methods are based on global oblique and orthogonal projections of the initial matrix residual onto a matrix Krylov subspace. We first derive the global full orthogonalization method and give its properties. The second method which is a global orthogonal projection method is the global generalized minimum residual method. We then give some properties of this new algorithm. We also show how to apply these methods for solving the Lyapunov matrix equation. Finally, numerical examples will be given.