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

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.