Nonnegative Polynomial with no Certificate of Nonnegativity in the Simplicial Bernstein Basis
Numerical Analysis
2017-10-17 v1 Systems and Control
Abstract
This paper presents a nonnegative polynomial that cannot be represented with nonnegative coefficients in the simplicial Bernstein basis by subdividing the standard simplex. The example shows that Bernstein Theorem cannot be extended to certificates of nonnegativity for polynomials with zeros at isolated points.
Keywords
Cite
@article{arxiv.1710.05735,
title = {Nonnegative Polynomial with no Certificate of Nonnegativity in the Simplicial Bernstein Basis},
author = {Christoffer Sloth},
journal= {arXiv preprint arXiv:1710.05735},
year = {2017}
}