Geodesic
Approximating optimal point configurations for multivariate polynomial interpolation
Electronic transactions on numerical analysis, Tome 42 (2014), pp. 41-63
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 
@article{ETNA_2014__42__a7,
     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},
     year = {2014},
     volume = {42},
     zbl = {1298.65025},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2014__42__a7/}
}
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%A Sorber,  Laurent
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%F ETNA_2014__42__a7
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/