Faster algorithms for computing Hong's bound on absolute positiveness

Kurt Mehlhorn; Saurabh Ray

doi:10.1016/j.jsc.2010.02.002

Faster algorithms for computing Hong's bound on absolute positiveness

Kurt Mehlhorn, Saurabh Ray

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

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 language	English
Pages (from-to)	677-683
Number of pages	7
Journal	Journal of Symbolic Computation
Volume	45
Issue number	6
DOIs	https://doi.org/10.1016/j.jsc.2010.02.002
State	Published - 1 Jan 2010
Externally published	Yes

Keywords

Absolute positiveness
Geometric computing
Hongs bound
Multivariate polynomials

ASJC Scopus subject areas

Algebra and Number Theory
Computational Mathematics

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10.1016/j.jsc.2010.02.002

Cite this

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title = "Faster algorithms for computing Hong's bound on absolute positiveness",

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.",

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AB - 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.

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KW - Geometric computing

KW - Hongs bound

KW - Multivariate polynomials

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Faster algorithms for computing Hong's bound on absolute positiveness

Abstract

Keywords

ASJC Scopus subject areas

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