Determining roots of real-valued functions of a single variable over a distributed network

Abstract

Many problems require determining the root of a real-valued function of a single variable. Maple and Marletta presented a parallel algorithm that can be used to determine a simple root of such functions. High levels of efficiency were proved for functions satisfying a set of conditions. In this work we present a framework and subsequently a piece of software to evaluate the performance of their algorithm under various conditions and for functions with varying characteristics. We also consider the effects of implementing the algorithm over a heterogeneous network, presenting results and recommendations.