# On the Various Bisection Methods Derived from Vincent’s Theorem

Akritas, Alkiviadis; Strzeboński, Adam; Vigklas, Panagiotis

Serdica Journal of Computing (2008)

- Volume: 2, Issue: 1, page 89-104
- ISSN: 1312-6555

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topAkritas, Alkiviadis, Strzeboński, Adam, and Vigklas, Panagiotis. "On the Various Bisection Methods Derived from Vincent’s Theorem." Serdica Journal of Computing 2.1 (2008): 89-104. <http://eudml.org/doc/11455>.

@article{Akritas2008,

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.},

author = {Akritas, Alkiviadis, Strzeboński, Adam, Vigklas, Panagiotis},

journal = {Serdica Journal of Computing},

keywords = {Vincent’s Theorem; Real Root Isolation Method; Bisection Method; Continued Fraction Method; Descartes’ Method; Modified Uspensky’s Method; numerical examples; polynomial roots; Vincent's theorem; real root isolation method; bisection method; continued fraction method; Descartes' method; modified Uspensky's method},

language = {eng},

number = {1},

pages = {89-104},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {On the Various Bisection Methods Derived from Vincent’s Theorem},

url = {http://eudml.org/doc/11455},

volume = {2},

year = {2008},

}

TY - JOUR

AU - Akritas, Alkiviadis

AU - Strzeboński, Adam

AU - Vigklas, Panagiotis

TI - On the Various Bisection Methods Derived from Vincent’s Theorem

JO - Serdica Journal of Computing

PY - 2008

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 2

IS - 1

SP - 89

EP - 104

AB - 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.

LA - eng

KW - Vincent’s Theorem; Real Root Isolation Method; Bisection Method; Continued Fraction Method; Descartes’ Method; Modified Uspensky’s Method; numerical examples; polynomial roots; Vincent's theorem; real root isolation method; bisection method; continued fraction method; Descartes' method; modified Uspensky's method

UR - http://eudml.org/doc/11455

ER -

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