Skip to main content
1 of 2
Will Jagy
  • 25.7k
  • 2
  • 65
  • 121

You might like this one, I do not know if the entire link will fit, anyway

Journal of Approximation Theory Volume 104, Issue 1, Pages 1-182 (May 2000)

Uniqueness of the Gaussian Quadrature for a Ball Pages 21-44

B. Bojanova, 1 and G. Petrovab, 2

Department of Mathematics, University of Sofia, Boulevard James Boucher 5, 1164, Sofia, Bulgariaf1

Department of Mathematics, University of South Carolina, Columbia, South Carolina, 29208, U.S.A., f2 Received 8 June 1999; accepted 22 October 1999. ; Available online 26 March 2002.

Abstract

We construct a formula for numerical integration of functions over the unit ball in Image d that uses n Radon projections of these functions and is exact for all algebraic polynomials in Image d 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.

Author Keywords: Gauss quadrature formula; orthogonal polynomials; highest degree of precision

Will Jagy
  • 25.7k
  • 2
  • 65
  • 121