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math.OC2024
Least multivariate Chebyshev polynomials on diagonally determined sets
Mareike Dressler, Simon Foucart, Mioara Joldes +3
We consider a new multivariate generalization of the classical monic (univariate) Chebyshev polynomial that minimizes the uniform norm on the interval . Let be the…
math.OC2024
Optimization-Aided Construction of Multivariate Chebyshev Polynomials
Mareike Dressler, Simon Foucart, Mioara Joldes +3
This article is concerned with an extension of univariate Chebyshev polynomials of the first kind to the multivariate setting, where one chases best approximants to specific monomi…
math.OC2024
The link between -norm approximation and effective Positivstellensatze for the hypercube
Etienne de Klerk, Juan Vera Lizcano
The Schmüdgen's Positivstellensatz gives a certificate to verify positivity of a strictly positive polynomial on a compact, basic, semi-algebraic set $\mathbf{K} \subset \mathb…