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# Convergence of Multilevel Stationary Gaussian Convolution

Hubbert, Simon and Levesley, J. (2019) Convergence of Multilevel Stationary Gaussian Convolution. In: Radu, F. and Kumar, K. and Berre, I. and Nordbotten, J. and Pop, I. (eds.) Numerical Mathematics and Advanced Applications - ENUMATH 2017. Lecture Notes in Computational Science and Engineering 126. Springer, pp. 83-92. ISBN 9783319964140.

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## Abstract

In this paper we give a short note showing convergence rates for multilevel periodic approximation of smooth functions by multilevel Gaussian convolution. We will use the Gaussian scaling in the convolution at the finest level as a proxy for degrees of freedom $d$ in the model. We will show that, for functions in the native space of the Gaussian, convergence is of the order $d^{-\frac{\ln(d)}{\ln(2)}}$. This paper provides a baseline for what should be expected in discrete convolution, which will be the subject of a follow up paper.

Item Type: Book Section Birkbeck Schools and Departments > School of Business, Economics & Informatics > Economics, Mathematics and Statistics Simon Hubbert 11 Jun 2019 14:21 01 Aug 2019 00:34 http://eprints.bbk.ac.uk/id/eprint/21751