Near optimal Tchakaloff meshes for compact sets with Markov exponent 2

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. 

Vianello M. (2018) "Near optimal Tchakaloff meshes for compact sets with Markov exponent 2 " Dolomites Research Notes on Approximation, 11(4), 79-83. DOI: 10.14658/PUPJ-DRNA-2018-4-8  
Year of Publication
2018
Journal
Dolomites Research Notes on Approximation
Volume
11
Issue Number
4
Start Page
79
Last Page
83
Date Published
11/2018
ISSN Number
2035-6803
Serial Article Number
8
DOI
10.14658/PUPJ-DRNA-2018-4-8
Issue
Section
SpecialIssue4