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Keywords = Caratheodory-Tchakaloff discrete measure compression

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15 pages, 959 KB  
Article
dCATCH—A Numerical Package for d-Variate near G-Optimal Tchakaloff Regression via Fast NNLS
by Monica Dessole, Fabio Marcuzzi and Marco Vianello
Mathematics 2020, 8(7), 1122; https://doi.org/10.3390/math8071122 - 9 Jul 2020
Cited by 6 | Viewed by 2936
Abstract
We provide a numerical package for the computation of a d-variate near G-optimal polynomial regression design of degree m on a finite design space X R d , by few iterations of a basic multiplicative algorithm followed by Tchakaloff-like compression of [...] Read more.
We provide a numerical package for the computation of a d-variate near G-optimal polynomial regression design of degree m on a finite design space X R d , by few iterations of a basic multiplicative algorithm followed by Tchakaloff-like compression of the discrete measure keeping the reached G-efficiency, via an accelerated version of the Lawson-Hanson algorithm for Non-Negative Least Squares (NNLS) problems. This package can solve on a personal computer large-scale problems where c a r d ( X ) × dim ( P 2 m d ) is up to 10 8 10 9 , being dim ( P 2 m d ) = 2 m + d d = 2 m + d 2 m . Several numerical tests are presented on complex shapes in d = 3 and on hypercubes in d > 3 . Full article
(This article belongs to the Special Issue Numerical Methods)
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