Public Domain Software: FGMRES


A Set of Flexible GMRES Routines for Real and Complex Arithmetics.

by   V. Frayssé    L. Giraud    S. Gratton

Last Release: July 2001 - Version 1.5
We propose an implementation of the flexible GMRES (FGMRES) (Saad, 1993) algorithm for both real and complex, single and double precision arithmetics suitable for serial, shared memory and distributed memory computers. FGMRES is a variant of the GMRES method with right preconditioning that enables the use of a different preconditioner at each step of the Arnoldi process. In particular, a few steps of GMRES can be used as a preconditioner for FGMRES. Click here for downloading the GMRES packages.
For the sake of simplicity, flexibility and efficiency the FGMRES solvers have been implemented 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, that is a well-known bottleneck of efficiency for the Krylov methods (related CERFACS technical report - TR/PA/98/07 (Gzipped PostCript 54 kB)). Finally the implemented stopping criterion is based on a normwise backward error.

Click here to download the User's Guide in postscript (Gzipped PostScript 78 KB) or pdf format.
Bugs or remarks should be mailed to the authors:  
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Commercial License
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Last Update: Aug 13, 2001