Acceleration of algebraically-converging Fourier series when the coefficients have series in powers of \(1/n\)
type: Item
instance of: scholarly article
title: Acceleration of algebraically-converging Fourier series when the coefficients have series in powers of \(1/n\)
zbMATH Open document ID: 1159.65112
author: John P. Boyd
published in: Journal of Computational Physics
publication date: 2009-03-09T00:00:00Z
Mathematics Subject Classification ID: 65T40
zbMATH DE Number: 5526441
zbMATH Keywords: pseudospectral method
zbMATH Keywords: spectral method
zbMATH Keywords: Gibbs phenomenon
zbMATH Keywords: numerical examples
zbMATH Keywords: Fourier cosine series
zbMATH Keywords: Lanczos-Krylov functions
zbMATH Keywords: Clausen functions
zbMATH Keywords: endpoint subtraction
MaRDI profile type: Publication
full work available at URL: j.jcp.2008.10.039
OpenAlex ID: W2020779581
cites work: Polynomial Fitting for Edge Detection in Irregularly Sampled Signals and Images
cites work: Error Estimates for Sine Series Expansions
cites work: A united approach to accelerating trigonometric expansions
cites work: On the application of pseudospectral FFT techniques to non‐periodic problems
cites work: The asymptotic Chebyshev coefficients for functions with logarithmic endpoint singularities: Mappings and singular basis functions
cites work: Sum-accelerated pseudospectral methods: The Euler-accelerated sinc algorithm
cites work: A lag-average generalization of Euler's method for accelerating series
cites work: Two comments on filtering (artificial viscosity) for Chebyshev and Legendre spectral and spectral element methods: Preserving boundary conditions and interpretation of the filter as a diffusion
cites work: Chebyshev and Fourier spectral methods.
cites work: On a method to evaluate Fourier-Bessel series with poor convergence properties and its application to linearized supersonic free jet flow
cites work: A Padé-based algorithm for overcoming the Gibbs phenomenon
cites work: Accurate Reconstructions of Functions of Finite Regularity from Truncated Fourier Series Expansions
cites work: On a high order numerical method for solving partial differential equations in complex geometries
cites work: On a high order numerical method for functions with singularities
cites work: Exponentially accurate approximations to piece-wise smooth periodic functions
cites work: Spectral Reconstruction of Piecewise Smooth Functions from Their Discrete Data
cites work: On the Gibbs Phenomenon and Its Resolution
cites work: On the Gibbs phenomenon. I: Recovering exponential accuracy from the Fourier partial sum of a nonperiodic analytic function
cites work: Generalization of the inverse polynomial reconstruction method in the resolution of the Gibbs phenomenon
cites work: Inverse polynomial reconstruction of two dimensional Fourier images
cites work: On the numerical convergence with the inverse polynomial reconstruction method for the resolution of the Gibbs phenomenon
cites work: Determination of the jumps of a bounded function by its Fourier series
cites work: Detecting the singularities of a function of \(V_p\) class by its integrated Fourier series
cites work: Evaluation of Noisy Data
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cites work: One- and two-dimensional lattice sums for the three-dimensional Helmholtz equation
cites work: Computational Techniques Based on the Lanczos Representation
cites work: The calculation of trigonometric Fourier coefficients
cites work: The Fourier Method for Nonsmooth Initial Data
cites work: Convergence acceleration of Fourier series by analytical and numerical application of Poisson's formula
cites work: On the analytical summation of Fourier series and its relation to the asymptotic behaviour of Fourier transforms
cites work: On a rational linear approximation of Fourier series for smooth functions
cites work: A convergence acceleration method of Fourier series
cites work: Convergence acceleration of orthogonal series
cites work: A pseudo-spectral FFT technique for non-periodic problems
cites work: Adaptive mollifiers for high resolution recovery of piecewise smooth data from its spectral information
cites work: Adaptive filters for piecewise smooth spectral data*
cites work: Optimal filter and mollifier for piecewise smooth spectral data
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cites work: Pseudospectral solution of atmospheric diffusion problems
cites work: A robust method for accurately representing nonperiodic functions given Fourier coefficient information
cites work: Local spline approximation of discontinuous functions and location of discontinuities, given low-order Fourier coefficient information.
DOI: 10.1016/J.JCP.2008.10.039
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description: scientific article; zbMATH DE number 5526441