On Optimal Designs for a d-Cube
Title | On Optimal Designs for a d-Cube |
Publication Type | Journal Article |
Year of Publication | 2022 |
Authors | Bos, L |
Journal | Dolomites Research Notes on Approximation |
Volume | 15 |
Issue | 4 |
Pagination | 20-34 |
Date Published | 12/2022 |
Publisher | Padova University Press |
Place Published | Padova, IT |
ISSN Number | 2035-6803 |
Abstract | We show that for the d-cube K = [−1,1]d ⊂ Rd , there is for degree 2 a symmetric optimal design supported on the discrete set consisting of the vertices, the edge midpoints and the origin with cardinality 2d + d2d−1 + 1. In general there is a continuum of possible optimal designs with, however, a support of larger cardinality. We also consider numerically the degree three case for the square [−1,1] ⊂ R2. Our calculations indicate that there is an optimal measure supported on 16 points but that these do not form a regular grid. |
URL | https://drna.padovauniversitypress.it/2022/4/3 |
DOI | 10.14658/pupj-drna-2022-4-3 |
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