Efficient implementation of bivariate interpolation and cubature at Padua points

Here we show four families of Padua points for interpolation at any even or odd degree n, and we present a stable and efficient implementation of the corresponding

In the present paper, we study the interpolation on the Padua points using an ideal theoretic approach, which considers the points as the variety of a polynomial ideal and it treats

From the general theory on quadrature formulas and polynomial ideals, it follows that the set of Padua points is a variety of a polynomial ideal generated by

We have recently proved that the Lebesgue constant of these points grows like log 2 (n), n being the de- gree, as with the best known points for the square, and we have imple- mented

In this paper we present a stable and efficient Fortran implementation of the Lagrange interpolation formula at the Padua points, with cost O(n 3 ) flops for the evaluation (once

Keywords: bivariate Lagrange interpolation, Padua points, bivariate Chebyshev or- thogonal basis, nontensorial Clenshaw-Curtis-like cubature, matrix product formula- tion, FFT. ∗

The Padua points, recently studied during an international collaboration at the University of Padua, are the first known example of near-optimal point set for bivariate polynomial

Abstract We have implemented in Matlab/Octave two fast algorithms for bivariate Lagrange interpolation at the so-called Padua points on rectangles, and the corresponding versions