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Convergence of Multilevel Stationary Gaussian Convolution

  • Simon Hubbert
  • Jeremy LevesleyEmail author
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 126)

Abstract

In this paper we give a short note showing convergence rates for 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.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Birkbeck, University of LondonLondonUK
  2. 2.Department of MathematicsUniversity of LeicesterLeicesterUK

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