Faster algorithms for computing Hong's bound on absolute positiveness

Kurt Mehlhorn, Saurabh Ray

Research output: Contribution to journalArticle

Abstract

We show how to compute Hongs bound for the absolute positiveness of a polynomial in d variables with maximum degree in O(nlogdn) time, where n is the number of non-zero coefficients. For the univariate case, we give a linear time algorithm. As a consequence, the time bounds for the continued fraction algorithm for real root isolation improve by a factor of δ.

Original languageEnglish (US)
Pages (from-to)677-683
Number of pages7
JournalJournal of Symbolic Computation
Volume45
Issue number6
DOIs
StatePublished - Jan 1 2010

Fingerprint

Fast Algorithm
Real Roots
Computing
Linear-time Algorithm
Continued fraction
Maximum Degree
Isolation
Univariate
Polynomials
Polynomial
Coefficient

Keywords

  • Absolute positiveness
  • Geometric computing
  • Hongs bound
  • Multivariate polynomials

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics

Cite this

Faster algorithms for computing Hong's bound on absolute positiveness. / Mehlhorn, Kurt; Ray, Saurabh.

In: Journal of Symbolic Computation, Vol. 45, No. 6, 01.01.2010, p. 677-683.

Research output: Contribution to journalArticle

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