Optimal Points for Cubature Rules and Polynomial Interpolation on a Square

Abstract

The nodes of certain minimal cubature rule are real common zeros of a set of orthogonal polynomials of degree $n$. They often consist of a well distributed set of points and interpolation polynomials based on them have desired convergence behavior. We report what is known and the theory behind by explaining the situation when the domain of integrals is a square.

to appear in Festschrift for the 80th Birthday of Ian Sloan