Approximation of a Multivariate Function of Bounded Variation from its Scattered Data

Fuente: arXiv
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Autore principale: Dachiraju, Rajesh
Natura: Preprint
Pubblicazione: 2020
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author Dachiraju, Rajesh
author_facet Dachiraju, Rajesh
contents This paper addresses the problem of approximating a function of bounded variation from its scattered data. Radial basis function(RBF) interpolation methods are known to approximate only functions in their native spaces, and to date, there has been no known proof that they can approximate functions outside the native space associated with the particular RBF being used. In this paper, we describe a scattered data interpolation method which can approximate any function of bounded variation from its scattered data as the data points grow dense. As the class of functions of bounded variation is a much wider class than the native spaces of the RBF, this method provides a crucial advantage over RBF interpolation methods.
format Preprint
id arxiv_https___arxiv_org_abs_2011_11258
institution arXiv
publishDate 2020
record_format arxiv
spellingShingle Approximation of a Multivariate Function of Bounded Variation from its Scattered Data
Dachiraju, Rajesh
Numerical Analysis
Analysis of PDEs
42A10 42A15 35C99
This paper addresses the problem of approximating a function of bounded variation from its scattered data. Radial basis function(RBF) interpolation methods are known to approximate only functions in their native spaces, and to date, there has been no known proof that they can approximate functions outside the native space associated with the particular RBF being used. In this paper, we describe a scattered data interpolation method which can approximate any function of bounded variation from its scattered data as the data points grow dense. As the class of functions of bounded variation is a much wider class than the native spaces of the RBF, this method provides a crucial advantage over RBF interpolation methods.
title Approximation of a Multivariate Function of Bounded Variation from its Scattered Data
topic Numerical Analysis
Analysis of PDEs
42A10 42A15 35C99
url https://arxiv.org/abs/2011.11258