Intervenant: Hassane Sadok (LMPA Joseph Liouville) Date et lieu: vendredi 12 mai à 16h en salle B014. Titre : Convergence properties and implementations of Block Krylov subspaces methods Résumé: Krylov subspace methods are widely used for the iterative solution of a large variety of linear systems of equations with one or several right hand sides or for solving nonsymmetric eigenvalue problems. The solution of linear systems of equations with several right-hand sides is considered. Approximate solutions are conveniently computed by block GMRES methods. We describe and study three variants of block GMRES. These methods are based on three implementations of the block Arnoldi method, which differ in their choice of inner product.. The Block GMRES is classically implemented by first applying the Arnoldi iteration as a block orthogonalization process to create a basis of the block Krylov space generated by the matrix of the system from the initial residual. Next, the method is solving a block least-squares problem, which is equivalent to solving several least squares problems implying the same Hessenberg matrix. These laters are usually solved by using a block updating procedure for the QR decomposition of the Hessenberg matrix based on Givens rotations. A more effective alternative was given by M. H. Gutknecht and T. Schmelzer which uses the Householder reflectors. We propose a new and simple implementation of the block GMRES algorithm, based on a generalization of Ayachour’s method given for the GMRES with a single right-hand side. Several numerical experiments are provided to illustrate the performance of the new implementation.