This paper presents a new preconditioning technique for the restarted GMRES algorithm. It is based on an invariant subspace approximation which is updated at each cycle. Numerical examples show that this deea-tion technique gives a more robust scheme than the restarted algorithm, at a low cost of operations and memory.
Iterative methods for solving linear systems of equations can be very eecient if the structure of the coeecient matrix can be exploited to accelerate the convergence of the iterative process. However, for classes of problems for which suitable preconditioners cannot be found or for which the iteration scheme does not converge, iterative techniques may be… (More)
1 Abstract In this paper it is shown how to adapt an existing package (VODE) for solving systems of ordinary diierential equations on serial computers to distributed memory parallel computers. The approach taken is based on waveform relaxation in which the problem is decomposed into a sequence of subproblems and which are then solved independently using… (More)
In this paper, modiications to the distributed memory waveform relaxation package developed by Burrage and Pohl 2], known as PWVODE, are considered. Various dynamic, adaptive and communication protocols are considered, and a number of numerical comparisons on a 96 node Intel Paragon are presented which show the eecacy of PWVODE.