On bivariate Gaussian cubature formulae

Gaussian extended cubature formulae for polyharmonic functions

The purpose of this paper is to show certain links between univariate interpolation by algebraic polynomials and the representation of polyharmonic functions. This allows us to construct cubature formulae for multivariate functions having highest order of precision with respect to the class of polyharmonic functions. We obtain a Gauss type cubature formula that uses m values of linear functiona...

Gaussian Cubature and Bivariate Polynomial Interpolation

Gaussian cubature is used to study bivariate polynomial interpolation based on the common zeros of quasi-orthogonal polynomials.

Gaussian Extended Cubature Formulae for Polyharmonic

Near-minimal cubature formulae on the disk

The construction of (near-)minimal cubature formulae on the disk is still a complicated subject on which many results have been published.We restrict ourselves to the case of radial weight functions and make use of a recent connection between cubature and the concept of multivariate spherical orthogonal polynomials to derive a new system of equations defining the nodes and weights of (near-)min...

New cubature formulae and hyperinterpolation

A new algebraic cubature formula of degree 2n + 1 for the product Chebyshev measure in the d-cube with ≈ nd/2d−1 nodes is established. The new formula is then applied to polynomial hyperinterpolation of degree n in three variables, in which coefficients of the product Chebyshev orthonormal basis are computed by a fast algorithm based on the 3dimensional FFT. Moreover, integration of the hyperin...