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• W2892593147 abstract "Spherical Gauss-Laguerre (SGL) basis functions, i. e., normalized functions of the type $L_{n-l-1}^{(l + 1/2)}(r^2) r^l Y_{lm}(vartheta,varphi)$, $|m| leq l < n in mathbb{N}$, $L_{n-l-1}^{(l + 1/2)}$ being a generalized Laguerre polynomial, $Y_{lm}$ a spherical harmonic, constitute an orthonormal polynomial basis of the space $L^2$ on $mathbb{R}^3$ with radial Gaussian (multivariate Hermite) weight $exp(-r^2)$. We have recently described fast Fourier transforms for the SGL basis functions based on an exact quadrature formula with certain grid points in $mathbb{R}^3$. In this paper, we present fast SGL Fourier transforms for scattered data. The idea is to employ well-known basal fast algorithms to determine a three-dimensional trigonometric polynomial that coincides with the bandlimited function of interest where the latter is to be evaluated. This trigonometric polynomial can then be evaluated efficiently using the well-known non-equispaced FFT (NFFT). We proof an error estimate for our algorithms and validate their practical suitability in extensive numerical experiments." @default.
• W2892593147 created "2018-10-05" @default.
• W2892593147 creator A5091400713 @default.
• W2892593147 date "2018-09-27" @default.
• W2892593147 modified "2023-09-27" @default.
• W2892593147 title "Fast SGL Fourier transforms for scattered data" @default.
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• W2892593147 hasPublicationYear "2018" @default.
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