Asynchronous parallel methods for enclosing solutions of nonlinear equations

Abstract

We consider interval arithmetic based parallel methods for enclosing solutions of nonlinear systems of equations, where processors are allowed to proceed asynchronously. We present a general study on the convergence of asynchronous iterations in interval spaces and apply them to a variety of methods for the nonlinear equations case. The convergence results turn out to be very similar to those known for synchronous methods. Several practical examples on shared memory architectures are included. The asynchronous methods sometimes perform substantially better than their synchronous counterparts.