Family of spectral filters for discontinuous problems
Journal of Scientific Computing
Journal of Computational and Applied Mathematics - Orthogonal polynomials and numerical methods
SIAM Journal on Numerical Analysis
On the Gibbs Phenomenon and Its Resolution
SIAM Review
Spectral methods in MatLab
Enhanced spectral viscosity approximations for conservation laws
Proceedings of the fourth international conference on Spectral and high order methods (ICOSAHOM 1998)
Detection of Edges in Spectral Data II. Nonlinear Enhancement
SIAM Journal on Numerical Analysis
The spectral signal processing suite
ACM Transactions on Mathematical Software (TOMS)
Chebyshev super spectral viscosity method for a fluidized bed model
Journal of Computational Physics
Determination of Optimal Parameters for the Chebyshev-Gegenbauer Reconstruction Method
SIAM Journal on Scientific Computing
Towards the resolution of the Gibbs phenomena
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Inverse Polynomial Reconstruction of Two Dimensional Fourier Images
Journal of Scientific Computing
Spectral Methods Based on Prolate Spheroidal Wave Functions for Hyperbolic PDEs
SIAM Journal on Numerical Analysis
Padé-Legendre Interpolants for Gibbs Reconstruction
Journal of Scientific Computing
Digital Total Variation Filtering as Postprocessing for Radial Basis Function Approximation Methods
Computers & Mathematics with Applications
Reconstruction of Piecewise Smooth Functions from Non-uniform Grid Point Data
Journal of Scientific Computing
Edge Detection Free Postprocessing for Pseudospectral Approximations
Journal of Scientific Computing
The digital TV filter and nonlinear denoising
IEEE Transactions on Image Processing
Edge Detection Free Postprocessing for Pseudospectral Approximations
Journal of Scientific Computing
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Global polynomial approximation methods applied to piecewise continuous functions exhibit the well-known Gibbs phenomenon. We summarize known methods to remove the Gibbs oscillations and present a collection of Matlab programs that implement the methods. The software features a Graphical User Interface that allows easy access to the postprocessing algorithms for benchmarking and educational purposes.