Constructing Positive Interpolatory Cubature Formulas
Numerical Analysis
2020-09-28 v1 Numerical Analysis
Classical Analysis and ODEs
Optimization and Control
Abstract
Positive interpolatory cubature formulas (CFs) are constructed for quite general integration domains and weight functions. These CFs are exact for general vector spaces of continuous real-valued functions that contain constants. At the same time, the number of data points -- all of which lie inside the domain of integration -- and cubature weights -- all positive -- is less or equal to the dimension of that vector space. The existence of such CFs has been ensured by Tchakaloff in 1957. Yet, to the best of the author's knowledge, this work is the first to provide a procedure to successfully construct them.
Cite
@article{arxiv.2009.11981,
title = {Constructing Positive Interpolatory Cubature Formulas},
author = {Jan Glaubitz},
journal= {arXiv preprint arXiv:2009.11981},
year = {2020}
}
Comments
17 pages