Batra, PrashantPrashantBatraSharma, VikramVikramSharma2019-12-022019-12-022010-06Journal of Symbolic Computation 6 (45): 617-628 (2010)http://hdl.handle.net/11420/3922We 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.en1095-855X20106617628ElsevierAbsolute positivenessMultivariate polynomialsRoot boundsMathematikJournal Article10.1016/j.jsc.2010.01.012Journal Article