Bivariate Lagrange interpolation at the Padua points: The generating curve approach

Abstract

We give a simple, geometric and explicit construction of bivariate interpolation at certain points in a square (called Padua points), giving compact formulas for their fundamental Lagrange polynomials. We show that the associated norms of the interpolation operator, i.e., the Lebesgue constants, have minimal order of growth of O ( ( log n ) 2 ) . To the best of our knowledge this is the first complete, explicit example of near optimal bivariate interpolation points.