Geodesic
Approximating optimal point configurations for multivariate polynomial interpolation
Electronic transactions on numerical analysis, Tome 42 (2014), pp. 41-63.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Efficient and effective algorithms are designed to compute the coordinates of nearly optimal points for multivariate polynomial interpolation on a general geometry. "Nearly optimal" refers to the property that the set of points has a Lebesgue constant near to the minimal Lebesgue constant with respect to multivariate polynomial interpolation on a finite region. The proposed algorithms range from cheap ones that produce point configurations with a reasonably low Lebesgue constant, to more expensive ones that can find point configurations for several two-dimensional shapes which have the lowest Lebesgue constant in comparison to currently known results.
Classification : 41A10, 65D05, 65D15, 65E05
Keywords: (nearly) optimal points, multivariate polynomial interpolation, Lebesgue constant, greedy add and update algorithms, weighted least squares, Vandermonde matrix, orthonormal basis 
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     author = {van Barel, Marc and Humet, Matthias and Sorber, Laurent},
     title = {Approximating optimal point configurations for multivariate polynomial interpolation},
     journal = {Electronic transactions on numerical analysis},
     pages = {41--63},
     publisher = {mathdoc},
     volume = {42},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2014__42__a7/}
}
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van Barel, Marc; Humet, Matthias; Sorber, Laurent. Approximating optimal point configurations for multivariate polynomial interpolation. Electronic transactions on numerical analysis, Tome 42 (2014), pp. 41-63. http://geodesic.mathdoc.fr/item/ETNA_2014__42__a7/