Improving the Performance of the Continued Fractions Method Using New Bounds of Positive Roots
Articles
A. G. G. Akritas
University of Thessaly, Greece
A. W. W. Strzebonski
Wolfram Research, Inc., USA
P. S. S. Vigklas
University of Thessaly, Greece
Published 2008-07-25
https://doi.org/10.15388/NA.2008.13.3.14557
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Keywords

Vincent’s theorem
polynomial real root isolation
continued fractions method
upper bounds on positive roots
linear and quadratic complexity bounds

How to Cite

Akritas, A.G.G., Strzebonski, A.W.W. and Vigklas, P.S.S. (2008) “Improving the Performance of the Continued Fractions Method Using New Bounds of Positive Roots”, Nonlinear Analysis: Modelling and Control, 13(3), pp. 265–279. doi:10.15388/NA.2008.13.3.14557.

Abstract

In this paper we compare four implementations of the Vincent-AkritasStrzebo´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 implementation using LMQ, the Quadratic complexity variant of our Local Max bound, achieved an overall average speed-up of 40 % over the original implementation using Cauchy’s linear bound.

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