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A new class of asynchronous iterative algorithms with order intervals

Authors: J. C. Miellou, D. El Baz and P. Spiteri
Journal: Math. Comp. 67 (1998), 237-255
MSC (1991): Primary 65N12, 65N55, 68Q10, 68Q22
MathSciNet review: 1432131
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Abstract: This paper deals with a new class of parallel asynchronous iterative algorithms for the solution of nonlinear systems of equations. The main feature of the new class of methods presented here is the possibility of flexible communication between processors. In particular partial updates can be exchanged. Approximation of the associated fixed point mapping is also considered. A detailed convergence study is presented. A connection with the Schwarz alternating method is made for the solution of nonlinear boundary value problems. Computational results on a shared memory multiprocessor IBM 3090 are briefly presented.

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Additional Information

J. C. Miellou
Affiliation: L.C.S. URA CNRS n$^{∘}$ 040741, Université de Franche-Comté, 16, Route de Gray, 25030 Besançon Cedex, France

D. El Baz
Affiliation: LAAS du CNRS L.P. CNRS 8001, 7, Avenue du Colonel Roche, 31077 Toulouse Cedex, France

P. Spiteri
Affiliation: ENSEEIHT-IRIT UA CNRS 1399, LIMA, Institut National Polytechnique de Tou- louse, 2, Rue Camichel, 31071 Toulouse Cedex, France

Keywords: Parallel iterative methods, asynchronous iterations, Schwarz alternating method, domain decomposition methods, boundary value problems
Received by editor(s): December 9, 1994
Received by editor(s) in revised form: January 26, 1996, and July 19, 1996
Article copyright: © Copyright 1998 American Mathematical Society