Uniqueness of the Gaussian Quadrature for a Ball Academic Article uri icon

abstract

  • We construct a formula for numerical integration of functions over the unit ball in Rd that uses n Radon projections of these functions and is exact for all algebraic polynomials in Rd of degree 2n-1. This is the highest algebraic degree of precision that could be achieved by an n term integration rule of this kind. We prove the uniqueness of this quadrature. In particular, we present a quadrature formula for a disk that is based on line integrals over n chords and integrates exactly all bivariate polynomials of degree 2n-1. © 2000 Academic Press.

author list (cited authors)

  • Bojanov, B., & Petrova, G.

citation count

  • 14

publication date

  • May 2000