Work

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

Year: 2019

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1904.00206

Authors: Dinh, Trung Hoa, Ho, Minh Toan, Le, Cong Trinh

Institutions: Troy University, Institute of Mathematics, Vietnam Academy of Science and Technology

Language: English

Topic: Advanced Optimization Algorithms Research

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Vietnam Institute for Advanced Study in Mathematics

OpenAlex ID: W2932726477

Cites: 18

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Related to: 10