GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical 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
Rounding Errors in Algebraic Processes
Rounding Errors in Algebraic Processes
ACM Transactions on Mathematical Software (TOMS)
International Journal of Computer Mathematics - Fast Iterative and Preconditioning Methods for Linear and Non-Linear Systems
Parallel algebraic domain decomposition solver for the solution of augmented systems
Advances in Engineering Software
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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.