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.
On Optimal Designs for a d-Cube
Bos L. (2022) "On Optimal Designs for a d-Cube " Dolomites Research Notes on Approximation, 15(4), 20-34. DOI: 10.14658/PUPJ-DRNA-2022-4-3
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Dolomites Research Notes on Approximation
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