On Interpolation Approximation: Convergence Rates for Polynomial Interpolation for Functions of Limited Regularity

DOI10.1137/15M1025281zbMath1342.65084arXiv1411.7746OpenAlexW2963568012MaRDI QIDQ5739967

Shuhuang Xiang

Publication date: 7 July 2016

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.7746

zbMATH Keywords

numerical examplesconvergence ratepolynomial interpolationPeano kernellimited regularityChebyshev pointGauss-Jacobi pointJacobi-Gauss-Lobatto pointstrongly normal point systemWainerman's lemma

Mathematics Subject Classification ID

Numerical interpolation (65D05) Interpolation in approximation theory (41A05) Approximation by polynomials (41A10)

Related Items (13)

On the optimal convergence rates of Chebyshev interpolations for functions of limited regularity ⋮ Jacobi collocation method and smoothing transformation for numerical solution of neutral nonlinear weakly singular Fredholm integro-differential equations ⋮ Fast multipole methods for approximating a function from sampling values ⋮ Optimal decay rates on the asymptotics of orthogonal polynomial expansions for functions of limited regularities ⋮ Series solution and Chebyshev collocation method for the initial value problem of Emden-Fowler equation ⋮ Fast computation of the spectral differentiation by the fast multipole method ⋮ Noniterative Computation of Gauss--Jacobi Quadrature ⋮ An accurate spectral method for the transverse magnetic mode of Maxwell equations in Cole-Cole dispersive media ⋮ Clenshaw-Curtis-type quadrature rule for hypersingular integrals with highly oscillatory kernels ⋮ A new spectral method using nonstandard singular basis functions for time-fractional differential equations ⋮ On the convergence rate of Hermite-Fejér interpolation ⋮ Efficient construction of FCC+ rules ⋮ On efficient computation of highly oscillatory retarded potential integral equations

Uses Software

• Matlab
• mctoolbox
• Chebfun
• Mulprec

Cites Work

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