Synchronous and Asynchronous Interval Newton-Schwarz Methods for a Class of Large Systems of Nonlinear Equations

Synchronous and Asynchronous Interval Newton-Schwarz Methods for a Class of Large Systems of... We introduce a class of parallel interval arithmetic iteration methods for nonlinear systems of equations, especially of the type Ax+ϕ(x) = f, ϕ diagonal, in R N . These methods combine enclosure and global convergence properties of Newton-like interval methods with the computational efficiency of parallel block iteration methods: algebraic forms of Schwarz-type methods which generalize both the well-known additive algebraic Schwarz Alternating Procedure and multisplitting methods. We discuss both synchronous and asynchronous variants. Besides enclosure and convergence properties, we present numerical results from a CRAY T3E. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

Synchronous and Asynchronous Interval Newton-Schwarz Methods for a Class of Large Systems of Nonlinear Equations

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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 2001 by Kluwer Academic Publishers
Subject
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1023/A:1011407223334
Publisher site
See Article on Publisher Site

Abstract

We introduce a class of parallel interval arithmetic iteration methods for nonlinear systems of equations, especially of the type Ax+ϕ(x) = f, ϕ diagonal, in R N . These methods combine enclosure and global convergence properties of Newton-like interval methods with the computational efficiency of parallel block iteration methods: algebraic forms of Schwarz-type methods which generalize both the well-known additive algebraic Schwarz Alternating Procedure and multisplitting methods. We discuss both synchronous and asynchronous variants. Besides enclosure and convergence properties, we present numerical results from a CRAY T3E.

Journal

Reliable ComputingSpringer Journals

Published: Oct 3, 2004

References

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