تقرير
Optimization-Aided Construction of Multivariate Chebyshev Polynomials
| العنوان: | Optimization-Aided Construction of Multivariate Chebyshev Polynomials |
|---|---|
| المؤلفون: | Dressler, Mareike, Foucart, Simon, Joldes, Mioara, de Klerk, Etienne, Lasserre, Jean Bernard, Xu, Yuan |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Optimization and Control, Mathematics - Numerical Analysis, 41A10, 65D15, 90C22 |
| الوصف: | 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 monomials by polynomials of lower degree relative to the uniform norm. Exploiting the Moment-SOS hierarchy, we devise a versatile semidefinite-programming-based procedure to compute such best approximants, as well as associated signatures. Applying this procedure in three variables leads to the values of best approximation errors for all mononials up to degree six on the euclidean ball, the simplex, and the cross-polytope. Furthermore, inspired by numerical experiments, we obtain explicit expressions for Chebyshev polynomials in two cases unresolved before, namely for the monomial $x_1^2 x_2^2 x_3$ on the euclidean ball and for the monomial $x_1^2 x_2 x_3$ on the simplex. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2405.10438 |
| رقم الأكسشن: | edsarx.2405.10438 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |