Reconstruction of a discontinuous function from a few Fourier coefficients using Bayesian estimation

DOI10.1007/BF02087960zbMath0840.65104MaRDI QIDQ1908492

Alex Solomonoff

Publication date: 30 June 1996

Published in: Journal of Scientific Computing (Search for Journal in Brave)

zbMATH Keywords

conservation lawsBayesian analysisBurgers equationGibbs phenomenonreconstruction algorithmspectral methodsGaussian probability distributionFourier series solutionsminimum-error algorithm

Mathematics Subject Classification ID

Foundations and philosophical topics in statistics (62A01) Hyperbolic conservation laws (35L65) Series solutions to PDEs (35C10) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items (9)

Pseudospectral Fourier reconstruction with the modified inverse polynomial reconstruction method ⋮ Finite Fourier frame approximation using the inverse polynomial reconstruction method ⋮ On the numerical convergence with the inverse polynomial reconstruction method for the resolution of the Gibbs phenomenon ⋮ Recovering exponential accuracy from non-harmonic Fourier data through spectral reprojection ⋮ A simple regularization of the polynomial interpolation for the resolution of the Runge phenomenon ⋮ Detection of edges from nonuniform Fourier data ⋮ A Hybrid Method for the Resolution of the Gibbs Phenomenon ⋮ Algebraic Fourier reconstruction of piecewise smooth functions ⋮ Complete algebraic reconstruction of piecewise-smooth functions from Fourier data

Cites Work

• Efficient implementation of essentially nonoscillatory shock-capturing schemes
• Family of spectral filters for discontinuous problems
• Numerical study of pseudospectral methods in shock wave applications
• Analysis of the Spectral Vanishing Viscosity Method for Periodic Conservation Laws
• Calculation of Gauss Quadrature Rules
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