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A new Look at one of the Bisection Methods Derived from Vincent's Theorem
 

Summary: A new Look at one of the Bisection Methods Derived from
Vincent's Theorem
or
There is no Descartes' Method
Alkiviadis G. Akritas
Department of Computer and Communication Engineering
University of Thessaly
Greece
akritas@uth.gr
Dedicated to the memory of James Victor Uspensky (1883-1947)1
Abstract 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.
Key Words: Vincent's theorem, isolation of the real roots, real root isolation meth-
ods, bisection method, continued fractions method, Descartes' method/solver, modified
Uspensky's method.

  

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

 

Collections: Computer Technologies and Information Sciences