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

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Reliable Computing

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 RN. 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.

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  1. Fachbereich Mathematik, Technische Universität Berlin, MA 6-4, D-10623, Berlin, Germany

    Hartmut Schwandt

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  1. Hartmut Schwandt
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Schwandt, H. Synchronous and Asynchronous Interval Newton-Schwarz Methods for a Class of Large Systems of Nonlinear Equations. Reliable Computing 7, 281–306 (2001). https://doi.org/10.1023/A:1011407223334

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