A hybrid GMRES/LS-Arnoldi method to accelerate the parallel solution of linear systems
We present a parallel hybrid asynchronous method to solve large sparse linear systems by the use of a large parallel machine. This method combines a parallel GMRES(m) algorithm with the least squares method that needs some eigenvalues obtained from a parallel Arnoldi algorithm. All of the algorithms run on different processors of an IBM SP3 or IBM SP4 computer simultaneously. This implementation of this hybrid method allows us to take advantage of the parallelism available and to accelerate the convergence by decreasing considerably the number of iterations. (c) 2006 Elsevier Ltd. All rights reserved.
gmres arnoldi parallelism least squares hybrid method linear algebra sparse matrices iterative method