Approximating optimal point configurations for multivariate polynomial interpolation

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.