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On the Various Bisection Methods Derived from Vincent's Alkiviadis G. Akritas, Adam W. Strzebonski and Panagiotis S. Vigklas

Summary: On the Various Bisection Methods Derived from Vincent's
Alkiviadis G. Akritas, Adam W. StrzeboŽnski and Panagiotis S. Vigklas
Dedicated to Professors Alberto Alesina and Massimo Galuzzi.1
Abstract: In 2000 A. Alesina and M. Galuzzi presented Vincent's theorem "from a
modern point of view" along with two new bisection methods derived from it, B and C.
Their profound understanding of Vincent's theorem is responsible for simplicity -- the
characteristic property of these two methods. In this paper we compare the performance
of these two new bisection methods -- i.e. the time they take, as well as the number of
intervals they examine in order to isolate the real roots of polynomials -- against that
of the well-known Vincent-Collins-Akritas method, which is the first bisection method
derived from Vincent's theorem back in 1976. Experimental results indicate that REL,
the fastest implementation of the Vincent-Collins-Akritas method, is still the fastest
of the three bisection methods, but the number of intervals it examines is almost the
same as that of B. Therefore, further research on speeding up B while preserving its
simplicity looks promising.
Key Words: Vincent's theorem, real root isolation method, bisection method, con-
tinued fraction method, Descartes' method, modified Uspensky's method
Category: 2000 Mathematics Subject Classification: 26C10, 12D05, 12D10, 12E05,


Source: Akritas, Alkiviadis G. - Department of Computer and Communication Engineering, University of Thessaly


Collections: Computer Technologies and Information Sciences