Near optimal Tchakaloff meshes for compact sets with Markov exponent 2

TitleNear optimal Tchakaloff meshes for compact sets with Markov exponent 2
Publication TypeJournal Article
Year of Publication2018
AuthorsVianello, M
JournalDolomites Research Notes on Approximation
Volume11
Issue4
Pagination79-83
Date Published11/2018
PublisherPadova University Press
Place PublishedPadova, IT
ISSN Number2035-6803
Keywordsconvex bodies, Lipschitz boundary, Markov inequality, near optimal polynomial meshes, NonNegative Least Squares, Tchakaloff Theorem, uniform interior cone condition
Abstract

By a discrete version of Tchakaloff Theorem on positive quadrature formulas, we prove that any real multidimensional compact set admitting a Markov polynomial inequality with exponent 2 possesses a near optimal polynomial mesh. This improves for example previous results on general convex bodies and starlike bodies with Lipschitz boundary, being applicable to any compact set satisfying a uniform interior cone condition. We also discuss two algorithmic approaches for the computation of near optimal Tchakaloff meshes in low dimension. 

URLhttps://drna.padovauniversitypress.it/2018/4/10
DOI10.14658/pupj-drna-2018-4-10