Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/376

 Title: On the Various Bisection Methods Derived from Vincent’s Theorem Authors: Akritas, AlkiviadisStrzeboński, AdamVigklas, Panagiotis Keywords: Vincent’s TheoremReal Root Isolation MethodBisection MethodContinued Fraction MethodDescartes’ MethodModified Uspensky’s Method Issue Date: 2008 Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences Citation: Serdica Journal of Computing, Vol. 2, No 1, (2008), 89p-104p Abstract: In 2000 A. Alesina and M. Galuzzi presented Vincent’s theorem “from a modern point of view” along with two new bisection methods derived from it, B and C. Their profound understanding of Vincent’s theorem is responsible for simplicity — the characteristic property of these two methods. In this paper we compare the performance of these two new bisection methods — i.e. the time they take, as well as the number of intervals they examine in order to isolate the real roots of polynomials — against that of the well-known Vincent-Collins-Akritas method, which is the first bisection method derived from Vincent’s theorem back in 1976. Experimental results indicate that REL, the fastest implementation of the Vincent-Collins-Akritas method, is still the fastest of the three bisection methods, but the number of intervals it examines is almost the same as that of B. Therefore, further research on speeding up B while preserving its simplicity looks promising. URI: http://hdl.handle.net/10525/376 ISSN: 1312-6555 Appears in Collections: Volume 2 Number 1

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