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Transactions of the American Mathematical Society

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Interpolation polynomials which give best order of approximation among continuously differentiable functions of arbitrary fixed order on $ [-1,\,+1]$


Author: A. K. Varma
Journal: Trans. Amer. Math. Soc. 200 (1974), 419-426
MSC: Primary 41A05
DOI: https://doi.org/10.1090/S0002-9947-1974-0369999-5
MathSciNet review: 0369999
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Abstract: The object of this paper is to show that there exists a polynomial $ {P_n}(x)$ of degree $ \leqslant 2n - 1$ which interpolates a given function exactly at the zeros of $ n$th Tchebycheff polynomial and for which $ \vert\vert f - {P_n}\vert\vert \leqslant {C_k}{w_k}(1/n,f)$ where $ {w_k}(1/n,f)$ is the modulus of continuity of $ f$ of $ k$th order.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1974-0369999-5
Keywords: Polynomial approximation, modulus of continuity, Hermite interpolation, typical means, Tchebycheff nodes
Article copyright: © Copyright 1974 American Mathematical Society