Bounding the Lebesgue function for Lagrange interpolatin in a simplex (Q798545)

It is the purpose of this paper to discuss the bound of the Lebesgue function for Lagrange interpolation in a simplex by polynomials of degree n in m variables. This paper shows that the Lebesgue function for the ''equally spaced'' points is bounded by \(\left( \begin{matrix} 2n-1\\ n\end{matrix} \right)\) independently of the dimension. Points with smaller norms are obtained considering those which maximize \(| VDM|\), a determinant similar to the Vandermonde determinant.They are calculated for low degrees and bounds of the given Lebesgue function.