Asynchronous iterations with flexible communication: contracting operators

Authors:
Didier El Baz;Andreas Frommer;Pierre Spiteri
Affiliations:
Laboratoire d'Analyse et d'Architecture des Systèmes du CNRS, 7, avenue du Colonel Roche, F-31077 Toulouse CEDEX 4, France;Fachbereich Mathematik und Naturwissenschaften, Universität Wuppertal, Gauss-Strasse 20 D-42097 Wuppertal, Germany;Ecole Nationale Supérieure d'Electrotechnique, d'Electronique, d'Informatique et d'Hydraulique de Toulouse, 2, rue Camichel, B.P. 7122, F-31071 Toulouse CEDEX 1, France
Venue:
Journal of Computational and Applied Mathematics
Year:
2005

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Abstract

The concept of flexible communication permits one to model efficient asynchronous iterations on parallel computers. This concept is particularly useful in two practical situations. Firstly, when communications are requested while a processor has completed the current update only partly, and secondly, in the context of inner/outer iterations, when processors are also allowed to make use of intermediate results obtained during the inner iteration in other processors.In the general case of nonlinear or linear fixed point problems, we give a global convergence results for asynchronous iterations with flexible communication whereby the iteration operators satisfy certain contraction hypotheses. In this manner we extend to a contraction context previous results obtained for monotone operators with respect to a partial ordering.