Abstract
We present an implementation of the Continued Fractions (CF) real root isolation method using a recently developed upper bound on the positive values of the roots of polynomials. Empirical results presented in this paper verify that this implementation makes the CF method always faster than the Vincent-Collins-Akritas bisection method, or any of its variants.
Misleadingly referred to (by several authors) initially as “modified Uspensky’s method” and recently as “Descartes’ method”.
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Akritas, A.G., Strzeboński, A.W., Vigklas, P.S. (2007). Advances on the Continued Fractions Method Using Better Estimations of Positive Root Bounds. In: Ganzha, V.G., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2007. Lecture Notes in Computer Science, vol 4770. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75187-8_3
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DOI: https://doi.org/10.1007/978-3-540-75187-8_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-75186-1
Online ISBN: 978-3-540-75187-8
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