# FLQ, the Fastest Quadratic Complexity Bound on the Values of Positive Roots of Polynomials

Akritas, Alkiviadis; Argyris, Andreas; Strzeboński, Adam

Serdica Journal of Computing (2008)

- Volume: 2, Issue: 2, page 145-162
- ISSN: 1312-6555

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topAkritas, Alkiviadis, Argyris, Andreas, and Strzeboński, Adam. "FLQ, the Fastest Quadratic Complexity Bound on the Values of Positive Roots of Polynomials." Serdica Journal of Computing 2.2 (2008): 145-162. <http://eudml.org/doc/11459>.

@article{Akritas2008,

abstract = {In this paper we present F LQ, a quadratic complexity bound on the values of the positive roots of polynomials. This bound is an extension of FirstLambda, the corresponding linear complexity bound and, consequently, it is derived from Theorem 3 below. We have implemented FLQ in the Vincent-Akritas-Strzeboński Continued Fractions method (VAS-CF) for the isolation of real roots of polynomials and compared its behavior with that of the theoretically proven best bound, LM Q. Experimental results
indicate that whereas F LQ runs on average faster (or quite faster) than LM Q, nonetheless the quality of the bounds computed by both is about the
same; moreover, it was revealed that when VAS-CF is run on our benchmark polynomials using F LQ, LM Q and min(F LQ, LM Q) all three versions run equally well and, hence, it is inconclusive which one should be used in the VAS-CF method.},

author = {Akritas, Alkiviadis, Argyris, Andreas, Strzeboński, Adam},

journal = {Serdica Journal of Computing},

keywords = {Vincent’s Theorem; Real Root Isolation Methods; Linear and Quadratic Complexity Bounds on the Values of the Positive Roots; numerical examples; Vincent's theorem; real root isolation methods; linear and quadratic complexity bounds; positive roots of polynomials; continued fractions method},

language = {eng},

number = {2},

pages = {145-162},

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

title = {FLQ, the Fastest Quadratic Complexity Bound on the Values of Positive Roots of Polynomials},

url = {http://eudml.org/doc/11459},

volume = {2},

year = {2008},

}

TY - JOUR

AU - Akritas, Alkiviadis

AU - Argyris, Andreas

AU - Strzeboński, Adam

TI - FLQ, the Fastest Quadratic Complexity Bound on the Values of Positive Roots of Polynomials

JO - Serdica Journal of Computing

PY - 2008

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 2

IS - 2

SP - 145

EP - 162

AB - In this paper we present F LQ, a quadratic complexity bound on the values of the positive roots of polynomials. This bound is an extension of FirstLambda, the corresponding linear complexity bound and, consequently, it is derived from Theorem 3 below. We have implemented FLQ in the Vincent-Akritas-Strzeboński Continued Fractions method (VAS-CF) for the isolation of real roots of polynomials and compared its behavior with that of the theoretically proven best bound, LM Q. Experimental results
indicate that whereas F LQ runs on average faster (or quite faster) than LM Q, nonetheless the quality of the bounds computed by both is about the
same; moreover, it was revealed that when VAS-CF is run on our benchmark polynomials using F LQ, LM Q and min(F LQ, LM Q) all three versions run equally well and, hence, it is inconclusive which one should be used in the VAS-CF method.

LA - eng

KW - Vincent’s Theorem; Real Root Isolation Methods; Linear and Quadratic Complexity Bounds on the Values of the Positive Roots; numerical examples; Vincent's theorem; real root isolation methods; linear and quadratic complexity bounds; positive roots of polynomials; continued fractions method

UR - http://eudml.org/doc/11459

ER -

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