Preconditioning parallel multisplittings for solving linear systems of equations

TitlePreconditioning parallel multisplittings for solving linear systems of equations
Publication TypeConference Papers
Year of Publication1992
AuthorsHuang C-M, O'Leary DP
Conference NameProceedings of the 6th international conference on Supercomputing
Date Published1992///
Conference LocationNew York, NY, USA
ISBN Number0-89791-485-6

We consider the practical implementation of Krylov subspace methods (conjugate gradients, GMRES, etc.) for parallel computers in the case where the preconditioning matrix is a multisplitting. The algorithm can be efficiently implemented by dividing the work into tasks that generate search directions and a single task that minimizes over the resulting subspace. Each task is assigned to a subset of processors. It is not necessary for the minimization task to send information to the direction generating tasks, and this leads to high utilization with a minimum of synchronization. We study the convergence properties of various forms of the algorithm.