Positive Polynomials on Closed Boxes

Authors

  • Marcio A. Diniz UFSCar
  • R. B. Stern
  • Luis E. Salazar

DOI:

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

Keywords:

positive polynomials, unit box, Bernstein polynomials

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 $\mathbb{R}^n$, $n>2$.

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Published

2019-12-02

How to Cite

Diniz, M. A., Stern, R. B., & Salazar, L. E. (2019). Positive Polynomials on Closed Boxes. Trends in Computational and Applied Mathematics, 20(3), 509. https://doi.org/10.5540/tema.2019.020.03.509

Issue

Section

Original Article