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

    Mehlhorn, Kurt ; Ray, Saurabh. / Faster algorithms for computing Hong's bound on absolute positiveness. In: Journal of Symbolic Computation. 2010 ; Vol. 45, No. 6. pp. 677-683.
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