Positive Polynomials on Closed Boxes

Marcio A. Diniz, R. B. Stern, Luis E. Salazar

Abstract


We present two different proofs that positive polynomials on closed boxes of $\mathbb{R}^2$ can be written as bivariate Bernstein polynomials with strictly positive coefficients.
Both strategies can be extended to prove the analogous result for polynomials that are positive on closed boxes of $\mathbb{R}^n$, $n>2$.


Keywords


positive polynomials, unit box, Bernstein polynomials

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DOI: https://doi.org/10.5540/tema.2019.020.03.509

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TEMA - Trends in Applied and Computational Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)
ISSN: 1677-1966  (print version),  2179-8451  (online version)

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