### 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 (US) |
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Pages (from-to) | 677-683 |

Number of pages | 7 |

Journal | Journal of Symbolic Computation |

Volume | 45 |

Issue number | 6 |

DOIs | |

State | Published - Jan 1 2010 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Algebra and Number Theory
- Computational Mathematics

### Cite this

*Journal of Symbolic Computation*,

*45*(6), 677-683. https://doi.org/10.1016/j.jsc.2010.02.002

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

Research output: Contribution to journal › Article

*Journal of Symbolic Computation*, vol. 45, no. 6, pp. 677-683. https://doi.org/10.1016/j.jsc.2010.02.002

}

TY - JOUR

T1 - Faster algorithms for computing Hong's bound on absolute positiveness

AU - Mehlhorn, Kurt

AU - Ray, Saurabh

PY - 2010/1/1

Y1 - 2010/1/1

N2 - 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.

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.

KW - Absolute positiveness

KW - Geometric computing

KW - Hongs bound

KW - Multivariate polynomials

UR - http://www.scopus.com/inward/record.url?scp=77951153034&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77951153034&partnerID=8YFLogxK

U2 - 10.1016/j.jsc.2010.02.002

DO - 10.1016/j.jsc.2010.02.002

M3 - Article

AN - SCOPUS:77951153034

VL - 45

SP - 677

EP - 683

JO - Journal of Symbolic Computation

JF - Journal of Symbolic Computation

SN - 0747-7171

IS - 6

ER -