The Bernstein constant and polynomial interpolation at the Chebyshev nodes.

DOI10.1006/jath.2002.3729zbMath1035.41015OpenAlexW2004859972MaRDI QIDQ1867520

Michael I. Ganzburg

Publication date: 2 April 2003

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/d04c6c39308bdfa6d6707c4d6bba7ad5805aae3f

zbMATH Keywords

Lagrange interpolationChebyshev nodesBernstein constant

Mathematics Subject Classification ID

Interpolation in approximation theory (41A05) Approximation by polynomials (41A10) Best constants in approximation theory (41A44)

Related Items (16)

A Hilbert transform representation of the error in Lagrange interpolation ⋮ Lagrange Interpolation and New Asymptotic Formulae for the Riemann Zeta Function ⋮ Strong asymptotics in Lagrange interpolation with equidistant nodes ⋮ Bernstein-type constants for approximation of \(| x |^\alpha\) by partial Fourier-Legendre and Fourier-Chebyshev sums ⋮ On estimates of uniform approximations by rational Fourier-Chebyshev integral operators for a certain choice of poles ⋮ The Riesz-Zygmund sums of Fourier-Chebyshev rational integral operators and their approximation properties ⋮ Scaling Limits of Polynomials and Entire Functions of Exponential Type ⋮ Unnamed Item ⋮ Best approximation and interpolation of \((1+(ax)^2)^{-1}\) and its transforms. ⋮ Polynomial interpolation, an \(L\)-function, and pointwise approximation of continuous functions ⋮ Extremal polynomials and entire functions of exponential type ⋮ On Interpolation Approximation: Convergence Rates for Polynomial Interpolation for Functions of Limited Regularity ⋮ Some extremal functions in Fourier analysis. III ⋮ Asymptotics of polynomial interpolation and the Bernstein constants ⋮ Asymptotics of the best polynomial approximation of \(|x|^{p}\) and of the best Laurent polynomial approximation of \(\text{sgn}(x)\) on two symmetric intervals ⋮ Asymptotic relations between interpolation differences and zeta functions

Cites Work

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• On the Bernstein conjecture in approximation theory
• Limit theorems for the best polynomial approximations in the \(L_ \infty\) metric
• Local convergence of Lagrange interpolation associated with equidistant nodes
• On Lagrange interpolatory parabolas to \(|x|^{\alpha}\) at equally spaced nodes
• On the divergence of Lagrange interpolation to \(| x|\)
• The divergence of Lagrange interpolation for \(|x|^\alpha\) at equidistant nodes
• On Lagrange interpolation with equidistant nodes
• Limit theorems for the best polynomial approximations in the L? metric
• On the approximation of certain functions by interpolating polynomials
• On Lagrange interpolation with equally spaced nodes
• Approximation constants in equidistant Lagrange interpolation

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