Laboratoire de Mathématiques Pures et Appliquées
Joseph Liouville

Séminaire et groupe de travail d’Approximation et Analyse matricielle du 12 mai 2017

Hassane Sadok (ULCO)

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.

Informations : 13:30 - 14:30 B014