Uniqueness of the Gaussian Quadrature for a Ball
نویسندگان
چکیده
We construct a formula for numerical integration of functions over the unit ball in R that uses n Radon projections of these functions and is exact for all algebraic polynomials in R 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
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تاریخ انتشار 2000