Interpolation lattices for hyperbolic cross trigonometric polynomials
type: Item
instance of: scholarly article
title: Interpolation lattices for hyperbolic cross trigonometric polynomials
zbMATH Open document ID: 1335.65105
author: Lutz Kämmerer
author: Stefan Kunis
author: Daniel Potts
published in: Journal of Complexity
publication date: 2012-01-10T00:00:00Z
review text: Sparse grid discretisations allow for a severe decrease in the number of degrees of freedom for high dimensional problems. The corresponding hyperbolic cross fast Fourier transform exhibits numerical instabilities already for moderate problem sizes. Therefore, the authors propose the use of oversampled lattice rules known from multivariate numerical integration, which allows for the highly effcient and perfectly stable evaluation and reconstruction of trigonometric polynomials using only one ordinary fast Fourier transform (FFT). Given is numerical evidence that reasonable small lattices exist such that this new method outperforms the sparse grid based hyperbolic cross FFT for realistic problem sizes.
reviewed by: Roza Aceska
Mathematics Subject Classification ID: 65T40
Mathematics Subject Classification ID: 42A15
Mathematics Subject Classification ID: 65T50
Mathematics Subject Classification ID: 65D32
zbMATH DE Number: 5996046
zbMATH Keywords: interpolation lattices
zbMATH Keywords: sparse grid
zbMATH Keywords: hyperbolic cross fast Fourier transform
zbMATH Keywords: multivariate numerical integration
zbMATH Keywords: trigonometric polynomials
describes a project that uses: NFFT
describes a project that uses: NHCFFT
describes a project that uses: NFFT3
MaRDI profile type: Publication
full work available at URL: j.jco.2011.05.002
OpenAlex ID: W1990197703
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DOI: 10.1016/J.JCO.2011.05.002
description: scientific article; zbMATH DE number 5996046