Approximation of a Multivariate Function of Bounded Variation from its Scattered Data
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Publication:6354318
arXiv2011.11258MaRDI QIDQ6354318
Publication date: 23 November 2020
Abstract: 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.
Trigonometric approximation (42A10) Trigonometric interpolation (42A15) Representations of solutions to partial differential equations (35C99)
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