On the Bernstein conjecture in approximation theory
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Publication:1105140
DOI10.1007/BF01890040zbMath0648.41013OpenAlexW1967779414WikidataQ123119332 ScholiaQ123119332MaRDI QIDQ1105140
Richard S. Varga, Amos J. Carpenter
Publication date: 1985
Published in: Constructive Approximation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf01890040
Best approximation, Chebyshev systems (41A50) Approximation by polynomials (41A10) Rate of convergence, degree of approximation (41A25)
Related Items (22)
Limit theorems in spline approximation ⋮ Best uniform rational approximation of \(x^ \alpha\) on \([0,1\).] ⋮ Barycentric-Remez algorithms for best polynomial approximation in the chebfun system ⋮ Analysis of Error Localization of Chebyshev Spectral Approximations ⋮ 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 ⋮ AAA Rational Approximation on a Continuum ⋮ Spectacularly large expansion coefficients in Müntz's theorem ⋮ Scaling Limits of Polynomials and Entire Functions of Exponential Type ⋮ Unnamed Item ⋮ Polynomial interpolation, an \(L\)-function, and pointwise approximation of continuous functions ⋮ Error Localization of Best $L_{1}$ Polynomial Approximants ⋮ Extremal polynomials and entire functions of exponential type ⋮ On Interpolation Approximation: Convergence Rates for Polynomial Interpolation for Functions of Limited Regularity ⋮ Best uniform rational approximation of 𝑥^{𝛼} on [0,1] ⋮ Asymptotics of polynomial interpolation and the Bernstein constants ⋮ Best approximation of functions like \(| x|^\lambda\exp (-A| x|^{-a})\) ⋮ Moduli of smoothness and best approximation of functions with singularities ⋮ On Lagrange interpolation with equally spaced nodes ⋮ On the approximation of certain functions by interpolating polynomials ⋮ No Jackson-type estimates for piecewise \(q\)-monotone, \(q \geq 3,\) trigonometric approximation ⋮ The Bernstein constant and polynomial interpolation at the Chebyshev nodes.
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