Bounds on absolute positiveness of multivariate polynomials

• Autores: Prashant Batra, Vikram Sharma
• Localización: Journal of symbolic computation, ISSN 0747-7171, Vol. 45, Nº 6, 2010, págs. 617-628
• Idioma: inglés
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• Resumen

  • 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.