Uniqueness of the Gaussian Quadrature for a Ball Academic Article

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.

authors

• Petrova, Guergana

published proceedings

• Journal of Approximation Theory

author list (cited authors)

• Bojanov, B., & Petrova, G.

citation count

• 15

complete list of authors

• Bojanov, B||Petrova, G

publication date

• January 2000

publisher

• Elsevier  Publisher

published in

• Journal of Approximation Theory  Journal

Digital Object Identifier (DOI)

• 10.1006/jath.1999.3442

start page

• 21

end page

• 44

volume

• 104

issue

• 1

URL

• http://dx.doi.org/10.1006/jath.1999.3442