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arXiv · 1904.00206

Some applications of Scherer-Hol's theorem for polynomial matrices

Trung Hoa Dinh·Minh Toan Ho·Cong Trinh Le
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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 P\'olya-Putinar-Vasilescu Positivstellensatz. Finally, we approximate positive semi-definite polynomial matrices using sums of squares.

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Trung Hoa Dinh, Minh Toan Ho, Cong Trinh Le. 2019-03-30. Some applications of Scherer-Hol's theorem for polynomial matrices. https://arxiv.org/abs/1904.00206

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