Some applications of Scherer-Hol's theorem for polynomial matrices
Abstract
In this paper we establish some applications of the Scherer-Hol's theorem for polynomial matrices. Firstly, we give a representation for polynomial matrices positive definite on subsets of compact polyhedra. Then we establish a Putinar-Vasilescu Positivstellensatz for homogeneous and non-homogeneous polynomial matrices. Next we propose a matrix version of the Pólya-Putinar-Vasilescu Positivstellensatz. Finally, we approximate positive semi-definite polynomial matrices using sums of squares.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2019
- DOI:
- 10.48550/arXiv.1904.00206
- arXiv:
- arXiv:1904.00206
- Bibcode:
- 2019arXiv190400206H
- Keywords:
-
- Mathematics - Algebraic Geometry;
- Mathematics - Operator Algebras;
- 15A48;
- 15A54;
- 11E25;
- 13J30;
- 14P10
- E-Print:
- 16 pages