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Global FOM and GMRES algorithms for matrix equations. (English) Zbl 0935.65024

Authors’ abstract: 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 (FOM) and give its properties. The second method which is a global orthogonal projection method is the global generalized minimum residual (GMRES) 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.

MSC:

65F10 Iterative numerical methods for linear systems
65F25 Orthogonalization in numerical linear algebra
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