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Bounds for Absolute Positiveness of Multivariate Polynomials

✍ Scribed by H. Hong

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 451 KB
Volume: 25
Category: Article
ISSN: 0747-7171
DOI: 10.1006/jsco.1997.0189

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✦ Synopsis

A multivariate polynomial P (x 1 , . . . , xn) with real coefficients is said to be absolutely positive from a real number B iff it and all of its non-zero partial derivatives of every order are positive for x 1 , . . . , xn ≥ B. We call such B a bound for the absolute positiveness of P . This paper provides a simple formula for computing such bounds. We also prove that the resulting bounds are guaranteed to be close to the optimal ones.

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