Abstract
We prove \({E_n}[f] < cons{t_k}{(\sqrt n )^{k + 1}}{2^{ - n}}(n + 1){!^{ - 1}}||{f^{(n - k)}}||\) (see (1), (2) for the relevant definitions). This bound is optimal with respect to the order. The degree of approximation is realized by interpolation with Chebyshev knots and by expansion in terms of Chebyshev polynomials.
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Braß, H. (1983). Restabschätzungen zur Polynomapproximation. In: Collatz, L., Meinardus, G., Werner, H. (eds) Numerical Methods of Approximation Theory, Vol. 7 / Numerische Methoden der Approximationstheorie, Band 7. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse numérique, vol 67. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6743-6_2
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DOI: https://doi.org/10.1007/978-3-0348-6743-6_2
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