Reconstruction of piecewise smooth functions from non-uniform grid point data
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Publication:879993
DOI10.1007/s10915-006-9099-3zbMath1113.65014OpenAlexW2083911739MaRDI QIDQ879993
Publication date: 10 May 2007
Published in: Journal of Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10915-006-9099-3
numerical examplesOrthogonal polynomialsGibbs phenomenonGegenbauer reconstructionnon-uniform grid point approximationreprojection
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Algorithms for approximation of functions (65D15) Numerical methods for trigonometric approximation and interpolation (65T40) Other transformations of harmonic type (42C20)
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Uses Software
Cites Work
- Parameter optimization and reduction of round off error for the Gegenbauer reconstruction method
- Robust reprojection methods for the resolution of the Gibbs phenomenon
- On the Gibbs phenomenon. I: Recovering exponential accuracy from the Fourier partial sum of a nonperiodic analytic function
- The quadrature discretization method (QDM) in the solution of the Schrödinger equation
- Towards the resolution of the Gibbs phenomena.
- Spectral method based on nonclassical basis functions: The advection-diffusion equation.
- Reducing the effects of noise in image reconstruction
- Adaptive mollifiers for high resolution recovery of piecewise smooth data from its spectral information
- Trouble with Gegenbauer reconstruction for defeating Gibbs' phenomenon: Runge phenomenon in the diagonal limit of Gegenbauer polynomial approximations
- Distributions of zeros of discrete and continuous polynomials from their recurrence relation
- Resolution properties of the Fourier method for discontinuous waves
- Enhanced spectral viscosity approximations for conservation laws
- Padé-Legendre interpolants for Gibbs reconstruction
- Fourier spectral simulations and Gegenbauer reconstructions for electromagnetic waves in the presence of a metal nanoparticle
- A class of orthogonal polynomials
- Optimal filter and mollifier for piecewise smooth spectral data
- Convergence of Spectral Methods for Nonlinear Conservation Laws
- On the Gibbs Phenomenon and Its Resolution
- Accurate Reconstructions of Functions of Finite Regularity from Truncated Fourier Series Expansions
- Determining Analyticity for Parameter Optimization of the Gegenbauer Reconstruction Method
- Polynomial Fitting for Edge Detection in Irregularly Sampled Signals and Images
- The Solution of Algebraic and Transcendental Equations by Iteration
- Spectral methods for hyperbolic problems
- A Padé-based algorithm for overcoming the Gibbs phenomenon
- A spectral solution of the Sturm-Liouville equation: Comparison of classical and nonclassical basis sets
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