Uniqueness of the Gaussian Quadrature for a Ball
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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.