1,567 research outputs found
Numerical hyperinterpolation over nonstandard planar regions
We discuss an algorithm (implemented in Matlab) that computes numerically total-degree bivariate orthogonal polynomials (OPs) given an algebraic cubature formula with positive weights, and constructs the orthogonal projection (hyperinterpolation) of a function sampled at the cubature nodes. The method is applicable to nonstandard regions where OPs are not known analytically, for example convex and concave polygons, or circular sections such as sectors, lenses and lunes
Some Results on the Complexity of Numerical Integration
This is a survey (21 pages, 124 references) written for the MCQMC 2014
conference in Leuven, April 2014. We start with the seminal paper of Bakhvalov
(1959) and end with new results on the curse of dimension and on the complexity
of oscillatory integrals. Some small errors of earlier versions are corrected
The Bivariate Normal Copula
We collect well known and less known facts about the bivariate normal
distribution and translate them into copula language. In addition, we prove a
very general formula for the bivariate normal copula, we compute Gini's gamma,
and we provide improved bounds and approximations on the diagonal.Comment: 24 page
Caratheodory-Tchakaloff Subsampling
We present a brief survey on the compression of discrete measures by
Caratheodory-Tchakaloff Subsampling, its implementation by Linear or Quadratic
Programming and the application to multivariate polynomial Least Squares. We
also give an algorithm that computes the corresponding Caratheodory-Tchakaloff
(CATCH) points and weights for polynomial spaces on compact sets and manifolds
in 2D and 3D
On Polyharmonic Interpolation
In the present paper we will introduce a new approach to multivariate
interpolation by employing polyharmonic functions as interpolants, i.e. by
solutions of higher order elliptic equations. We assume that the data arise
from or analytic functions in the ball We prove two main
results on the interpolation of or analytic functions in the
ball by polyharmonic functions of a given order of polyharmonicity
$p.
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