Learning Curves for Gaussian Processes via Numerical Cubature Integration

Gaussian Cubature and Bivariate Polynomial Interpolation

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

Numerical Cubature from Archimedes' Hat-box Theorem

Archimedes’ hat-box theorem states that uniform measure on a sphere projects to uniform measure on an interval. This fact can be used to derive Simpson’s rule. We present various constructions of, and lower bounds for, numerical cubature formulas using moment maps as a generalization of Archimedes’ theorem. We realize some well-known cubature formulas on simplices as projections of spherical de...

On the existence of minimum cubature formulas for Gaussian measure on R 2 of degree t supported by [ t 4 ] + 1 circles

In this paper we prove that there exists no minimum cubature formula of degree 4k and 4k+ 2 for Gaussian measure on R2 supported by k+ 1 circles for any positive integer k, except for two formulas of degree 4.

Gaussian Extended Cubature Formulae for Polyharmonic

Cubature formulae for spheres, simplices and balls

We obtain in explicit form the unique Gaussian cubature for balls (spheres) in Rn based on integrals over balls (spheres), centered at the origin, that integrates exactly all m-harmonic functions. In particular, this formula is exact for all polynomials in n variables of degree 2m − 1. A Gaussian cubature for simplices is also constructed. Upper bounds for the errors for certain smoothness clas...