Title: Chebyshev lattices, a unifying framework for cubature with Chebyshev weight function
Authors: Cools, Ronald *
Poppe, Koen * # ×
Issue Date: Jun-2011
Publisher: BIT Foundation
Series Title: BIT vol:51 issue:2 pages:275-288
Abstract: We present a multivariate extension to Clenshaw-Curtis quadrature based on Sloan’s hyperinterpolation theory. At the centre of it, a cubature rule for integrals with Chebyshev weight function is needed. We introduce so called Chebyshev lattices as a generalising framework for the multitude of point sets that have been discussed in this context. This framework provides a uniform notation that extends easily to higher dimensions. In this paper we describe many known point sets as Chebyshev lattices.

In the introduction we briefly explain how convergence results from hyperinter- polation can be used in this context. After introducing Chebyshev lattices and the associated cubature rules, we show how most of the two- and three-dimensional point sets in this context can be described with this notation. The not so commonly known blending formulae from Godzina, which explicitly describe point sets in any number of dimensions, also fit in perfectly.
ISSN: 0006-3835
Publication status: published
KU Leuven publication type: IT
Appears in Collections:NUMA, Numerical Analysis and Applied Mathematics Section
* (joint) first author
× corresponding author
# (joint) last author

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