Publisher DOI: 10.1016/j.jsc.2010.01.012
Title: Bounds on absolute positiveness of multivariate polynomials
Language: English
Authors: Batra, Prashant 
Sharma, Vikram 
Keywords: Absolute positiveness;Multivariate polynomials;Root bounds
Issue Date: Jun-2010
Publisher: Elsevier
Source: Journal of Symbolic Computation 6 (45): 617-628 (2010)
Journal or Series Name: Journal of symbolic computation 
Abstract (english): We propose and study a weighting framework for obtaining bounds on absolute positiveness of multivariate polynomials. It is shown that a well-known bound BG by Hong is obtainable in this framework, and w.r.t. any bound in this framework BG has a multiplicative overestimation which is at most linear in the number of variables. We also propose a general method to algorithmically improve any bound within the framework. In the univariate case, we derive the minimum number of weights necessary to obtain a bound with limited overestimation w.r.t. the absolute positiveness of the polynomial. © 2010 Elsevier Ltd.
ISSN: 1095-855X
Institute: Zuverlässiges Rechnen E-19 
Type: (wissenschaftlicher) Artikel
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