A New Look at One of the Bisection Methods Derived from Vincent's Theorem

Alkiviadis Akritas
University of Thessaly, Greece

In 1976, G.E. Collins and A.G. Akritas developed a bisection method for the
isolation of the real roots of polynomials.  Even though this method is based
on Vincent's theorem of 1836, credit to Vincent has been denied; to wit, from
1976 up until 1986 it was called ``modified Uspensky's method", whereas from
1986 to the present day it is being called either ``Collins-Akritas method" or
``Descartes' method".  In this paper we track the development of this bisection
method, show its relation to Vincent's theorem and justify the name
``Vincent-Collins-Akritas" given to it recently in France.