Handelman's Positivstellensatz for polynomial matrices positive definite on polyhedra
Algebraic Geometry
2017-08-10 v2
Abstract
In this paper we give a matrix version of Handelman's Positivstellensatz [1], representing polynomial matrices which are positive definite on convex, compact polyhedra. Moreover, we propose also a procedure to find such a representation. As a corollary of Handelman's theorem, we give a special case of Schm\"udgen's Positivstellensatz for polynomial matrices positive definite on convex, compact polyhedra.
Keywords
Cite
@article{arxiv.1603.07611,
title = {Handelman's Positivstellensatz for polynomial matrices positive definite on polyhedra},
author = {Công-Trình Lê and Thi-Hoa-Binh Du},
journal= {arXiv preprint arXiv:1603.07611},
year = {2017}
}
Comments
12 pages, minor revision, acknowledgement added, to be published in Positivity (2018)