Family of spectral filters for discontinuous problems
Journal of Scientific Computing
A modified Chebyshev pseudospectral method with an O(N–1) time step restriction
Journal of Computational Physics
Chebyshev--Legendre Super Spectral Viscosity Method for Nonlinear Conservation Laws
SIAM Journal on Numerical Analysis
Spectral methods in MatLab
A Hybrid Approach to Spectral Reconstruction of Piecewise Smooth Functions
Journal of Scientific Computing
Detection of Edges in Spectral Data II. Nonlinear Enhancement
SIAM Journal on Numerical Analysis
Inverse Polynomial Reconstruction of Two Dimensional Fourier Images
Journal of Scientific Computing
Digital Total Variation Filtering as Postprocessing for Radial Basis Function Approximation Methods
Computers & Mathematics with Applications
Detection of Edges in Spectral Data III--Refinement of the Concentration Method
Journal of Scientific Computing
Algorithm 899: The Matlab postprocessing toolkit
ACM Transactions on Mathematical Software (TOMS)
The digital TV filter and nonlinear denoising
IEEE Transactions on Image Processing
Algorithm 899: The Matlab postprocessing toolkit
ACM Transactions on Mathematical Software (TOMS)
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Pseudospectral Methods based on global polynomial approximation yield exponential accuracy when the underlying function is analytic. The presence of discontinuities destroys the extreme accuracy of the methods and the well-known Gibbs phenomenon appears. Several types of postprocessing methods have been developed to lessen the effects of the Gibbs phenomenon or even to restore spectral accuracy. The most powerful of the methods require that the locations of the discontinuities be precisely known. In this work we discuss postprocessing algorithms that are applicable when it is impractical, or difficult, or undesirable to pinpoint all discontinuity locations.