Algorithm 842 - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue ACM Transactions on Mathematical Software Année : 2005

Algorithm 842

Valérie Frayssé
  • Fonction : Auteur
Luc Giraud
  • Fonction : Auteur
Julien Langou
  • Fonction : Auteur

Résumé

In this article we describe our implementations of the GMRES algorithm for both real and complex, single and double precision arithmetics suitable for serial, shared memory and distributed memory computers. For the sake of portability, simplicity, flexibility and efficiency the GMRES solvers have been implemented in Fortran 77 using the reverse communication mechanism for the matrix-vector product, the preconditioning and the dot product computations. For distributed memory computation, several orthogonalization procedures have been implemented to reduce the cost of the dot product calculation, which is a well-known bottleneck of efficiency for the Krylov methods. Either implicit or explicit calculation of the residual at restart are possible depending on the actual cost of the matrix-vector product. Finally the implemented stopping criterion is based on a normwise backward error.
Fichier non déposé

Dates et versions

hal-03707406 , version 1 (28-06-2022)

Identifiants

Citer

Valérie Frayssé, Luc Giraud, Serge Gratton, Julien Langou. Algorithm 842. ACM Transactions on Mathematical Software, 2005, 31 (2), pp.228-238. ⟨10.1145/1067967.1067970⟩. ⟨hal-03707406⟩
44 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More