Bounds for positive roots of polynomials
Journal of Computational and Applied Mathematics
Elements of computer algebra with applications
Elements of computer algebra with applications
Fast algorithms for Taylor shifts and certain difference equations
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Bounds for absolute positiveness of multivariate polynomials
Journal of Symbolic Computation
Fundamental problems of algorithmic algebra
Fundamental problems of algorithmic algebra
Polynomial real root isolation using Descarte's rule of signs
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
Some inequalities about univariate polynomials
SYMSAC '81 Proceedings of the fourth ACM symposium on Symbolic and algebraic computation
Almost tight recursion tree bounds for the Descartes method
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Univariate polynomial real root isolation: continued fractions revisited
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Complexity of real root isolation using continued fractions
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Complexity analysis of algorithms in algebraic computation
Complexity analysis of algorithms in algebraic computation
On the complexity of real root isolation using continued fractions
Theoretical Computer Science
New bounds for the Descartes method
Journal of Symbolic Computation
Isolating real roots of real polynomials
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Experimental evaluation and cross-benchmarking of univariate real solvers
Proceedings of the 2009 conference on Symbolic numeric computation
Continued fraction expansion of real roots of polynomial systems
Proceedings of the 2009 conference on Symbolic numeric computation
On the Complexity of Reliable Root Approximation
CASC '09 Proceedings of the 11th International Workshop on Computer Algebra in Scientific Computing
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
Theoretical Computer Science
A simple but exact and efficient algorithm for complex root isolation
Proceedings of the 36th international symposium on Symbolic and algebraic computation
SqFreeEVAL: An (almost) optimal real-root isolation algorithm
Journal of Symbolic Computation
On the computing time of the continued fractions method
Journal of Symbolic Computation
Near optimal tree size bounds on a simple real root isolation algorithm
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
Improved bounds for the CF algorithm
Theoretical Computer Science
| Hi-index | 5.23 |
In this paper, we provide polynomial bounds on the worst case bit-complexity of two formulations of the continued fraction algorithm. In particular, for a square-free integer polynomial of degree n with coefficients of bit-length L, we show that the bit-complexity of Akritas' formulation is O@?(n^8L^3), and the bit-complexity of a formulation by Akritas and Strzebonski is O@?(n^7L^2); here O@? indicates that we are omitting logarithmic factors. The analyses use a bound by Hong to compute the floor of the smallest positive root of a polynomial, which is a crucial step in the continued fraction algorithm. We also propose a modification of the latter formulation that achieves a bit-complexity of O@?(n^5L^2).