Analysis of Error Localization of Chebyshev Spectral Approximations
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Publication:6040291
DOI10.1137/22m1481452zbMath1528.41016arXiv2106.03456OpenAlexW4367055221MaRDI QIDQ6040291
Publication date: 24 May 2023
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2106.03456
best approximationspointwise error estimatesspectral differentiationerror localizationChebyshev projectionsChebyshev interpolantsLegendre projections
Best approximation, Chebyshev systems (41A50) Approximation by polynomials (41A10) Rate of convergence, degree of approximation (41A25)
Related Items (4)
Parameter choice strategies for error expressions and the numerical stability of Tikhonov-regularized approximation formulae ⋮ Optimal error estimates for Chebyshev approximations of functions with endpoint singularities in fractional spaces ⋮ New error bounds for Legendre approximations of differentiable functions ⋮ Superconvergence points for higher-order derivative interpolation and its applications in spectral collocation method
Cites Work
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- Superconvergence of Jacobi-Gauss-type spectral interpolation
- On the convergence rate of Clenshaw-Curtis quadrature for integrals with algebraic endpoint singularities
- Optimal error estimates for Legendre expansions of singular functions with fractional derivatives of bounded variation
- Multivariate modified Fourier series and application to boundary value problems
- On the Bernstein conjecture in approximation theory
- Asymptotic expansions of the Hurwitz--Lerch zeta function
- Superconvergence in Galerkin finite element methods
- Asymptotic expansion of Fourier coefficients associated to functions with low continuity
- Pointwise error estimate of the Legendre expansion: the known and unknown features
- How much faster does the best polynomial approximation converge than Legendre projection?
- Optimal decay rates on the asymptotics of orthogonal polynomial expansions for functions of limited regularities
- Finding the Zeros of a Univariate Equation: Proxy Rootfinders, Chebyshev Interpolation, and the Companion Matrix
- Spectral Methods
- On the convergence rate of a modified Fourier series
- From high oscillation to rapid approximation I: modified Fourier expansions
- Spectral Methods in MATLAB
- Barycentric Lagrange Interpolation
- The numerical stability of barycentric Lagrange interpolation
- Collocation Methods for Volterra Integral and Related Functional Differential Equations
- Superconvergence Points of Polynomial Spectral Interpolation
- Is Gauss Quadrature Better than Clenshaw–Curtis?
- Spectral Methods
- Coefficients in Series Expansions for Certain Classes of Functions
- Pointwise error estimates and local superconvergence of Jacobi expansions
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