Bounds on absolute positiveness of multivariate polynomials

Publikationstyp
Journal Article
Date Issued
2010-06
Sprache
English
Author(s)
Batra, Prashant  orcid-logo
Sharma, Vikram  
Institut
Zuverlässiges Rechnen E-19  
TORE-URI
http://hdl.handle.net/11420/3922
Journal
Journal of symbolic computation  
Volume
45
Issue
6
Start Page
617
End Page
628
Citation
Journal of Symbolic Computation 6 (45): 617-628 (2010)
Publisher DOI
10.1016/j.jsc.2010.01.012
Scopus ID
2-s2.0-77951254722
Publisher
Elsevier
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.
Subjects
Absolute positiveness
Multivariate polynomials
Root bounds
DDC Class
510: Mathematik