Symbolicnumeric Gaussian cubature rules Universiteit Antwerpen
It is well known that Gaussian cubature rules are related to multivariate orthogonal polynomials. The cubature rules found in the literature use common zeroes of some linearly independent set of products of basically univariate polynomials. We show how a new family of multivariate orthogonal polynomials, so-called spherical orthogonal polynomials, leads to symbolicnumeric Gaussian cubature rules in a very natural way. They can be used for the ...