Preconditioning parallel multisplittings for solving linear systems of equations

Authors:
Chiou-Ming Huang;Dianne P. O'Leary
Affiliations:
-;-
Venue:
ICS '92 Proceedings of the 6th international conference on Supercomputing
Year:
1992

Citing 4
Cited 0

Parallel and distributed computation: numerical methods

Parallel and distributed computation: numerical methods
An updating algorithm for subspace tracking

An updating algorithm for subspace tracking
A black box generalized conjugate gradient solver with inner iterations and variable-step preconditioning

SIAM Journal on Matrix Analysis and Applications
Preconditioning parallel multisplittings for solving systems of equations

Preconditioning parallel multisplittings for solving systems of equations

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Abstract

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.