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

Author

Listed:
  • 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)

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 .

Suggested Citation

  • Monica Dessole & Fabio Marcuzzi & Marco Vianello, 2020. "dCATCH—A Numerical Package for d-Variate near G-Optimal Tchakaloff Regression via Fast NNLS," Mathematics, MDPI, vol. 8(7), pages 1-15, July.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:7:p:1122-:d:382335
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    References listed on IDEAS

    as
    1. Len Bos & Federico Piazzon & Marco Vianello, 2020. "Near G-optimal Tchakaloff designs," Computational Statistics, Springer, vol. 35(2), pages 803-819, June.
    2. de Klerk, Etienne & Laurent, Monique, 2019. "A survey of semidefinite programming approaches to the generalized problem of moments and their error analysis," Other publications TiSEM d956492f-3e25-4dda-a5e2-e, Tilburg University, School of Economics and Management.
    3. Dette, Holger & Pepelyshev, Andrey & Zhigljavsky, Anatoly, 2008. "Improving updating rules in multiplicative algorithms for computing D-optimal designs," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 312-320, December.
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