The Upper Bound for the Lebesgue Constant for Lagrange Interpolation in Equally Spaced Points of the Triangle (2209.10142v1)

Abstract: An upper bound for the Lebesgue constant (the supremum norm) of the operator of interpolation of a function in equally spaced points of a triangle by a polynomial of total degree less than or equal to n is obtained. Earlier, the rate of increase of the Lebesgue constants with respect to n for an arbitrary d-dimensional simplex was established by the author. The explicit upper bound proved in this article refines this result for d=2.