Subdivision Algorithms for Complex Root Isolation: Empirical Comparisons

Abstract

This thesis deals with the application of subdivision based algorithms to the problem of isolating the roots of a complex polynomial. We provide a comprehensive comparison of the performance of three interval arithmetic based predicates (the interval Newton, Krawczyk and Hansen-Sengupta operators) with predicates based on complex analysis (the CEVAL algorithm and Yakoubsohn’s approach). In addition, we include a treatment of the mathematical theory behind these operators.