Summary: Nonlinear Analysis: Modelling and Control, 2008, Vol. 13, No. 3, 265­279
Improving the Performance of the Continued Fractions
Method Using New Bounds of Positive Roots
A. G. Akritas1
, A. W. Strzebo´nski2
, P. S. Vigklas1
1
University of Thessaly, Department of Computer and Communication Engineering
GR-38221 Volos, Greece
{akritas, pviglas}@uth.gr
2
Wolfram Research, Inc., 100 Trade Center Drive, Champaign, IL 61820, USA
adams@wolfram.com
Received: 13.02.2008 Revised: 09.06.2008 Published online: 28.08.2008
Abstract. In this paper we compare four implementations of the Vincent-Akritas-
Strzebo´nski Continued Fractions (VAS-CF) real root isolation method using four different
(two linear and two quadratic complexity) bounds on the values of the positive roots
of polynomials. The quadratic complexity bounds were included to see if the quality
of their estimates compensates for their quadratic complexity. Indeed, experimentation
on various classes of special and random polynomials revealed that the VAS-CF

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

Collections: Computer Technologies and Information Sciences