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Geometric weakly admissible meshes, discrete least squares approximations and approximate Fekete points


Authors: L. Bos, J.-P. Calvi, N. Levenberg, A. Sommariva and M. Vianello
Journal: Math. Comp. 80 (2011), 1623-1638
MSC (2010): Primary 41A10, 41A63, 65D05, 65D15, 65Y20
DOI: https://doi.org/10.1090/S0025-5718-2011-02442-7
Published electronically: January 19, 2011
MathSciNet review: 2785471
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Abstract: Using the concept of Geometric Weakly Admissible Meshes (see §2 below) together with an algorithm based on the classical QR factorization of matrices, we compute efficient points for discrete multivariate least squares approximation and Lagrange interpolation.


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Additional Information

L. Bos
Affiliation: Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada T2N 1N4

J.-P. Calvi
Affiliation: Institut de Mathématiques de Toulouse, Université Paul Sabatier, 32062, Toulouse Cedex 9, France

N. Levenberg
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana, 47405

A. Sommariva
Affiliation: Department of Pure and Applied Mathematics, University of Padova, 35121 Padova, Italy

M. Vianello
Affiliation: Department of Pure and Applied Mathematics, University of Padova, 35121 Padova, Italy

DOI: https://doi.org/10.1090/S0025-5718-2011-02442-7
Keywords: Admissible meshes, discrete least squares approximation, approximate Fekete points, multivariate polynomial interpolation
Received by editor(s): February 10, 2009
Received by editor(s) in revised form: April 18, 2010
Published electronically: January 19, 2011
Additional Notes: The first author was supported in part by NSERC.
The last three authors were supported by the “ex-$60%$” funds and by the project “Interpolation and Extrapolation: new algorithms and applications” (2009/10) of the University of Padova, and by the INdAM GNCS
Article copyright: © Copyright 2011 American Mathematical Society

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