Improved bounds for the CF algorithm

Authors:
Elias P. Tsigaridas
Affiliations:
-
Venue:
Theoretical Computer Science
Year:
2013

Citing 20
Cited 0

Real zeroes of polynomials

Computer algebra: symbolic and algebraic computation (2nd ed.)
Fast algorithms for Taylor shifts and certain difference equations

ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Solving a Polynomial Equation: Some History and Recent Progress

SIAM Review
Bounds for absolute positiveness of multivariate polynomials

Journal of Symbolic Computation
Fundamental problems of algorithmic algebra

Fundamental problems of algorithmic algebra
Univariate polynomials: nearly optimal algorithms for numerical factorization and root-finding

Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
Optimal search for rationals

Information Processing Letters
Efficient isolation of polynomial's real roots

Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on linear algebra and arithmetic, Rabat, Morocco, 28-31 May 2001
Almost tight recursion tree bounds for the Descartes method

Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Implementations of a New Theorem for Computing Bounds for Positive Roots of Polynomials

Computing
Univariate polynomial real root isolation: continued fractions revisited

ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Real root-finding

Proceedings of the 2007 international workshop on Symbolic-numeric computation
On the complexity of real root isolation using continued fractions

Theoretical Computer Science
Real Algebraic Numbers: Complexity Analysis and Experimentation

Reliable Implementation of Real Number Algorithms: Theory and Practice
Complexity of real root isolation using continued fractions

Theoretical Computer Science
New bounds for the Descartes method

Journal of Symbolic Computation
Faster algorithms for computing Hong's bound on absolute positiveness

Journal of Symbolic Computation
Random polynomials and expected complexity of bisection methods for real solving

Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
A deterministic algorithm for isolating real roots of a real polynomial

Journal of Symbolic Computation
A worst-case bound for topology computation of algebraic curves

Journal of Symbolic Computation

Quantified Score

Hi-index	5.23

Visualization

Abstract

We consider the problem of isolating the real roots of a square-free polynomial with integer coefficients using the classic variant of the continued fraction algorithm (CF), introduced by Akritas. We compute a lower bound on the positive real roots of univariate polynomials using an exponential search. This allows us to derive a worst-case bound of O@?"B(d^4@t^2) for isolating the real roots of a polynomial with integer coefficients using the classic variant of CF, where d is the degree of the polynomial and @t the maximum bitsize of its coefficients. This improves the previous bound of Sharma by a factor of d^3 and matches the bound derived by Mehlhorn and Ray for another variant of CF which is combined with subdivision; it also matches the worst-case bound of the classical subdivision-based solvers sturm, descartes, and bernstein.