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This paper is concerned with Lagrange interpolation by total degreepolynomials in moderate dimensions. In particular, we are interested incharacterising the optimal choice of points for the interpolation problem,where we define the optimal interpolation points as those which minimise theLebesgue constant. We give a novel algorithm for numerically computing thelocation of the optimal points, which is independent of the shape of the domainand does not require computations with Vandermonde matrices. We perform anumerical study of the growth of the minimal Lebesgue constant with respect tothe degree of the polynomials and the dimension, and report the lowest valuesknown as yet of the Lebesgue constant in the unit cube and the unit ball in upto 10 dimensions.

Optimal Point Sets for Total Degree Polynomial Interpolation in Moderate Dimensions