dCATCH—A Numerical Package for d-Variate near G-Optimal Tchakaloff Regression via Fast NNLS

Monica Dessole, Fabio Marcuzzi and Marco Vianello
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Monica Dessole: Department of Mathematics “Tullio Levi Civita”, University of Padova, Via Trieste 63, 35131 Padova, Italy
Fabio Marcuzzi: Department of Mathematics “Tullio Levi Civita”, University of Padova, Via Trieste 63, 35131 Padova, Italy
Marco Vianello: Department of Mathematics “Tullio Levi Civita”, University of Padova, Via Trieste 63, 35131 Padova, Italy

Mathematics, 2020, vol. 8, issue 7, 1-15

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 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 .

Keywords: multivariate polynomial regression designs; G-optimality; D-optimality; multiplicative algorithms; G-efficiency; Caratheodory-Tchakaloff discrete measure compression; Non-Negative Least Squares; accelerated Lawson-Hanson solver (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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