Real root isolation of multi-exponential polynomials with application

Authors:
Ming Xu;Liangyu Chen;Zhenbing Zeng;Zhi-bin Li
Affiliations:
Shanghai Key Laboratory of Trustworthy Computing;Shanghai Key Laboratory of Trustworthy Computing;Shanghai Key Laboratory of Trustworthy Computing;Shanghai Key Laboratory of Trustworthy Computing
Venue:
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
Year:
2010

Citing 6
Cited 1

Real zeroes of polynomials

Computer algebra: symbolic and algebraic computation (2nd ed.)
Elements of computer algebra with applications

Elements of computer algebra with applications
Partial Cylindrical Algebraic Decomposition for quantifier elimination

Journal of Symbolic Computation
Symbolic Reachability Computation for Families of Linear Vector Fields

Journal of Symbolic Computation
Univariate polynomial real root isolation: continued fractions revisited

ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Deciding polynomial-exponential problems

Proceedings of the twenty-first international symposium on Symbolic and algebraic computation

Symbolic termination analysis of solvable loops

Journal of Symbolic Computation

Quantified Score

Hi-index	0.00

Visualization

Abstract

Real root isolation problem is to compute a list of disjoint intervals, each containing a distinct real root and together containing all. Traditional methods and tools often attack the root isolation for ordinary polynomials. However many other complex systems in engineering are modeling with non-ordinary polynomials. In this paper, we extend the pseudo-derivative sequences and Budan–Fourier theorem for multi-exponential polynomials to estimate the bounds and counts of all real roots. Furthermore we present an efficient algorithm for isolating all real roots under given minimum root separation. As a proof of serviceability, the reachability of linear systems with real eigenvalues only is approximately computable by this algorithm.