Degree Bounds for Polynomial Verification of the Matrix Cube Problem

Details Degree Bounds for Polynomial Verification of the Matrix Cube Problem Degree Bounds for Polynomial Verification of the Matrix Cube Problem

2006-04-26

arxiv.org/abs/math/0604573v1

Mathematics

Optimization and Control

Scientific paper

In this paper we consider the problem of how to computationally test whether
a matrix inequality is positive semidefinite on a semialgebraic set. We propose
a family of sufficient conditions using the theory of matrix Positivstellensatz
refutations. When the semialgebraic set is a hypercube, we give bounds on the
degree of the required certificate polynomials.

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