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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Hubbert, S., Levesley, J. (2019). Convergence of Multilevel Stationary Gaussian Convolution. In: Radu, F., Kumar, K., Berre, I., Nordbotten, J., Pop, I. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2017. ENUMATH 2017. Lecture Notes in Computational Science and Engineering, vol 126. Springer, Cham. https://doi.org/10.1007/978-3-319-96415-7_5
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DOI: https://doi.org/10.1007/978-3-319-96415-7_5
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