|Publisher DOI:||10.1016/j.jsc.2010.01.012||Title:||Bounds on absolute positiveness of multivariate polynomials||Language:||English||Authors:||Batra, Prashant
|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.||URI:||http://hdl.handle.net/11420/3922||ISSN:||1095-855X||Institute:||Zuverlässiges Rechnen E-19||Type:||(wissenschaftlicher) Artikel|
|Appears in Collections:||Publications without fulltext|
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