Acceleration of algebraically-converging Fourier series when the coefficients have series in powers of \(1/n\)
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Publication:1005376
DOI10.1016/j.jcp.2008.10.039zbMath1159.65112OpenAlexW2020779581MaRDI QIDQ1005376
Publication date: 9 March 2009
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jcp.2008.10.039
pseudospectral methodnumerical examplesGibbs phenomenonspectral methodClausen functionsFourier cosine seriesendpoint subtractionLanczos-Krylov functions
Related Items (14)
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Cites Work
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- Sum-accelerated pseudospectral methods: The Euler-accelerated sinc algorithm
- On the numerical convergence with the inverse polynomial reconstruction method for the resolution of the Gibbs phenomenon
- One- and two-dimensional lattice sums for the three-dimensional Helmholtz equation
- The asymptotic Chebyshev coefficients for functions with logarithmic endpoint singularities: Mappings and singular basis functions
- Family of spectral filters for discontinuous problems
- On the Gibbs phenomenon. I: Recovering exponential accuracy from the Fourier partial sum of a nonperiodic analytic function
- Pseudospectral solution of atmospheric diffusion problems
- A pseudo-spectral FFT technique for non-periodic problems
- Exponentially accurate approximations to piece-wise smooth periodic functions
- A convergence acceleration method of Fourier series
- 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
- Determination of the jumps of a bounded function by its Fourier series
- On a high order numerical method for solving partial differential equations in complex geometries
- Local spline approximation of discontinuous functions and location of discontinuities, given low-order Fourier coefficient information.
- Detecting the singularities of a function of \(V_p\) class by its integrated Fourier series
- A robust method for accurately representing nonperiodic functions given Fourier coefficient information
- Adaptive mollifiers for high resolution recovery of piecewise smooth data from its spectral information
- Generalization of the inverse polynomial reconstruction method in the resolution of the Gibbs phenomenon
- A united approach to accelerating trigonometric expansions
- A lag-average generalization of Euler's method for accelerating series
- The calculation of trigonometric Fourier coefficients
- Convergence acceleration of orthogonal series
- Inverse polynomial reconstruction of two dimensional Fourier images
- On a rational linear approximation of Fourier series for smooth functions
- Computational Techniques Based on the Lanczos Representation
- Optimal filter and mollifier for piecewise smooth spectral data
- Error Estimates for Sine Series Expansions
- The Fourier Method for Nonsmooth Initial Data
- Convergence acceleration of Fourier series by analytical and numerical application of Poisson's formula
- On the analytical summation of Fourier series and its relation to the asymptotic behaviour of Fourier transforms
- On the Gibbs Phenomenon and Its Resolution
- Spectrally Accurate Solution of Nonperiodic Differential Equations by the Fourier--Gegenbauer Method
- On a high order numerical method for functions with singularities
- Spectral Reconstruction of Piecewise Smooth Functions from Their Discrete Data
- Analysis and Application of Fourier–Gegenbauer Method to Stiff Differential Equations
- On the application of pseudospectral FFT techniques to non‐periodic problems
- On a method to evaluate Fourier-Bessel series with poor convergence properties and its application to linearized supersonic free jet flow
- Accurate Reconstructions of Functions of Finite Regularity from Truncated Fourier Series Expansions
- Evaluation of Noisy Data
- Polynomial Fitting for Edge Detection in Irregularly Sampled Signals and Images
- Adaptive filters for piecewise smooth spectral data*
- A Padé-based algorithm for overcoming the Gibbs phenomenon
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