GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
A flexible inner-outer preconditioned GMRES algorithm
SIAM Journal on Scientific Computing
A comparison of preconditioned nonsymmetric Krylov methods on a large-scale MIMD machine
SIAM Journal on Scientific Computing
Parallel implementation of a multiblock method with approximate subdomain solution
Applied Numerical Mathematics
An updated set of basic linear algebra subprograms (BLAS)
ACM Transactions on Mathematical Software (TOMS)
On computing givens rotations reliably and efficiently
ACM Transactions on Mathematical Software (TOMS)
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
On the Influence of the Orthogonalization Scheme on the Parallel Performance of GMRES
Euro-Par '98 Proceedings of the 4th International Euro-Par Conference on Parallel Processing
Theory of Inexact Krylov Subspace Methods and Applications to Scientific Computing
SIAM Journal on Scientific Computing
Inexact Krylov Subspace Methods for Linear Systems
SIAM Journal on Matrix Analysis and Applications
Inexact Matrix-Vector Products in Krylov Methods for Solving Linear Systems: A Relaxation Strategy
SIAM Journal on Matrix Analysis and Applications
ACM Transactions on Mathematical Software (TOMS)
Rounding Errors in Algebraic Processes
Rounding Errors in Algebraic Processes
SIAM Journal on Scientific Computing
Convergence in Backward Error of Relaxed GMRES
SIAM Journal on Scientific Computing
| Hi-index | 0.00 |
In this article we describe our implementations of the FGMRES 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 FGMRES 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 Krylov methods. Furthermore, either implicit or explicit calculation of the residual at restart is possible depending on the actual cost of the matrix-vector product. Finally, the implemented stopping criterion is based on a normwise backward error.