Near optimal Tchakaloff meshes for compact sets with Markov exponent 2
| Title | Near optimal Tchakaloff meshes for compact sets with Markov exponent 2 |
| Publication Type | Journal Article |
| Year of Publication | 2018 |
| Authors | Vianello, M |
| Journal | Dolomites Research Notes on Approximation |
| Volume | 11 |
| Issue | 4 |
| Pagination | 79-83 |
| Date Published | 11/2018 |
| Publisher | Padova University Press |
| Place Published | Padova, IT |
| ISSN Number | 2035-6803 |
| Keywords | convex 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. |
| URL | https://drna.padovauniversitypress.it/2018/4/10 |
| DOI | 10.14658/pupj-drna-2018-4-10 |
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