Gibbs phenomenon and its removal for a class of orthogonal expansions
From MaRDI portal
Publication:533707
DOI10.1007/s10543-010-0301-5zbMath1394.41008OpenAlexW2026422355MaRDI QIDQ533707
Publication date: 4 May 2011
Published in: BIT (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10543-010-0301-5
Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58) Numerical summation of series (65B10)
Related Items
Gibbs phenomenon removal by adding Heaviside functions, On the convergence of expansions in polyharmonic eigenfunctions, Gibbs phenomenon for Fourier partial sums on \(\mathbb{Z}_p\), Fourier tools are much more powerful than commonly thought, Unnamed Item, Generalized sampling and the stable and accurate reconstruction of piecewise analytic functions from their Fourier coefficients, On the Convergence of the Quasi-Periodic Approximations on a Finite Interval
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On the convergence of expansions in polyharmonic eigenfunctions
- Multivariate modified Fourier series and application to boundary value problems
- Acceleration of algebraically-converging Fourier series when the coefficients have series in powers of \(1/n\)
- On the Gibbs phenomenon. I: Recovering exponential accuracy from the Fourier partial sum of a nonperiodic analytic function
- The resolution of the Gibbs phenomenon for ``spliced functions in one and two dimensions
- A comparison of numerical algorithms for Fourier extension of the first, second, and third kinds
- Equiconvergence theorems for differential operators
- The calculation of trigonometric Fourier coefficients
- Univariate modified Fourier methods for second order boundary value problems
- On the convergence rate of a modified Fourier series
- A spectral collocation method for the Laplace and modified Helmholtz equations in a convex polygon
- On the Fourier Extension of Nonperiodic Functions
- Convergence acceleration of modified Fourier series in one or more dimensions
- Impossibility of Fast Stable Approximation of Analytic Functions from Equispaced Samples
- From high oscillation to rapid approximation II: expansions in Birkhoff series
- Computational Techniques Based on the Lanczos Representation
- From high oscillation to rapid approximation I: modified Fourier expansions
- Accelerating Convergence of Eigenfunction Expansions
- Accurate and Efficient Reconstruction of Discontinuous Functions from Truncated Series Expansions
- On the Gibbs Phenomenon and Its Resolution
- On a high order numerical method for functions with singularities
- Practical Extrapolation Methods
- Accurate Reconstructions of Functions of Finite Regularity from Truncated Fourier Series Expansions
- The spectral problem for a class of highly oscillatory Fredholm integral operators
- Filters, mollifiers and the computation of the Gibbs phenomenon
- Adjusted Forms of the Fourier Coefficient Asymptotic Expansion and Applications in Numerical Quadrature
- A Padé-based algorithm for overcoming the Gibbs phenomenon
