Bounds on absolute positiveness of multivariate polynomials

Authors:
Prashant Batra;Vikram Sharma
Affiliations:
Institute for Computer Technology, Hamburg University of Technology, 21071 Hamburg, Germany;Max Planck Institute for Informatics, 66123 Saarbrücken, Germany
Venue:
Journal of Symbolic Computation
Year:
2010

Citing 6
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Abstract

We propose and study a weighting framework for obtaining bounds on absolute positiveness of multivariate polynomials. It is shown that a well-known bound B"G by Hong is obtainable in this framework, and w.r.t. any bound in this framework B"G 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.