Asymptotic coefficients and errors for Chebyshev polynomial approximations with weak endpoint singularities: effects of different bases

DOI10.1007/s11425-021-1974-xzbMath1505.65019arXiv2103.11841OpenAlexW3137254578WikidataQ114222405 ScholiaQ114222405MaRDI QIDQ2679073

Yanyan Li

Publication date: 18 January 2023

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2103.11841

zbMATH Keywords

interpolationleast squares methodChebyshev polynomialendpoint singularities

Mathematics Subject Classification ID

Trigonometric approximation (42A10) Numerical interpolation (65D05) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Algorithms for approximation of functions (65D15)

Related Items (3)

Comparisons of best approximations with Chebyshev expansions for functions with logarithmic endpoint singularities ⋮ Optimal error estimates for Chebyshev approximations of functions with endpoint singularities in fractional spaces ⋮ A brief introduction to pseudo-spectral methods: application to diffusion problems

Uses Software

• DLMF

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The relationships between Chebyshev, Legendre and Jacobi polynomials: the generic superiority of Chebyshev polynomials and three important exceptions
• On the convergence rate of Clenshaw-Curtis quadrature for integrals with algebraic endpoint singularities
• Large-degree asymptotics and exponential asymptotics for Fourier, Chebyshev and Hermite coefficients and Fourier transforms
• Bernstein's asymptotic best bound for the kth derivative of a polynomial
• Chebyshev domain truncation is inferior to Fourier domain truncation for solving problems on an infinite interval
• Stabilization techniques for spectral methods
• Chebyshev and Legendre spectral methods in algebraic manipulation languages
• On the equivalence between basis recombination and boundary bordering formulations for spectral collocation methods in rectangular domains
• Asymptotic expansion of Fourier coefficients associated to functions with low continuity
• A gyroscopic polynomial basis in the sphere
• Optimal decay rates on the asymptotics of orthogonal polynomial expansions for functions of limited regularities
• Error estimates for Clenshaw-Curtis quadrature
• On the Optimal Estimates and Comparison of Gegenbauer Expansion Coefficients
• Solving Transcendental Equations
• Spectral Methods for Time-Dependent Problems
• Error Estimates for Sine Series Expansions
• On the Convergence Rates of Gauss and Clenshaw--Curtis Quadrature for Functions of Limited Regularity
• Convergence Rates on Spectral Orthogonal Projection Approximation for Functions of Algebraic and Logarithmatic Regularities
• Optimal error estimates for Chebyshev approximations of functions with limited regularity in fractional Sobolev-type spaces
• Is Gauss Quadrature Better than Clenshaw–Curtis?
• Asymptotic Estimates of Fourier Coefficients
• Coefficients in Series Expansions for Certain Classes of Functions
• The Evaluation and Estimation of the Coefficients in the Chebyshev Series Expansion of a Function

This page was built for publication: Asymptotic coefficients and errors for Chebyshev polynomial approximations with weak endpoint singularities: effects of different bases