English

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}
}