Nonnegative Polynomial with no Certificate of Nonnegativity in the Simplicial Bernstein Basis
arXiv:1710.057351 citationsh-index: 16
AI Analysis
This resolves a theoretical question in polynomial optimization and approximation theory, showing limitations of the Bernstein basis for certifying nonnegativity.
The paper presents a nonnegative polynomial that cannot be represented with nonnegative coefficients in the simplicial Bernstein basis, even after subdivision, disproving a potential extension of the Bernstein theorem for certificates of nonnegativity.
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.