Computing Fekete and Lebesgue points: Simplex, square, disk☆

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Abstract

We have computed point sets with maximal absolute value of the Vandermonde determinant (Fekete points) or minimal Lebesgue constant (Lebesgue points) on three basic bidimensional compact sets: the simplex, the square, and the disk. Using routines of the Matlab Optimization Toolbox, we have obtained some of the best bivariate interpolation sets known so far.

Keywords

Interpolation
Fekete Points
Lebesgue Points
Simplex
Square
Disk

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Work supported by the “ex-60 % ” funds and by the project “Interpolation and Extrapolation: new algorithms and applications” of the University of Padova, and by the INdAM GNCS.

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