Interpolation polynomials which give best order of approximation among continuously differentiable functions of arbitrary fixed order on $[-1, +1]$
HTML articles powered by AMS MathViewer
- by A. K. Varma PDF
- Trans. Amer. Math. Soc. 200 (1974), 419-426 Request permission
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 $||f - {P_n}|| \leqslant {C_k}{w_k}(1/n,f)$ where ${w_k}(1/n,f)$ is the modulus of continuity of $f$ of $k$th order.References
-
P. L. Butzer, On approximation theory (Proc. Conf. Oberwolfach, 1963), Birkhäuser, Basel, 1964. MR 31 #2537.
- Géza Freud, Über ein Jacksonsches interpolationsverfahren, On Approximation Theory (Proceedings of Conference in Oberwolfach, 1963), Birkhäuser, Basel, 1964, pp. 227–232 (German). MR 0182826
- S. B. Stečkin, On the order of the best approximations of continuous functions, Izvestiya Akad. Nauk SSSR. Ser. Mat. 15 (1951), 219–242 (Russian). MR 0041959
- S. B. Stečkin, The approximation of periodic functions by Fejér sums, Trudy Mat. Inst. Steklov. 62 (1961), 48–60 (Russian). MR 0162085
- A. K. Varma, The approximation of functions by certain trigonometric interpolation polynomials, Approximation theory (Proc. Internat. Sympos., Univ. Texas, Austin, Tex., 1973) Academic Press, New York, 1973, pp. 511–515. MR 0333550 —, Trigonometric interpolation polynomials which gives best order of approximation among continuously differentiable functions, Proc. Internat. Sympos. Approximation Theory (Poznań, Poland, 1972) (to appear).
- A. Zygmund, The approximation of functions by typical means of their Fourier series, Duke Math. J. 12 (1945), 695–704. MR 15539 —, Trigonometric series. Vols. 1, 2, 2nd rev. ed., Cambridge Univ. Press, New York, 1959. MR 21, #6498.
Additional Information
- © Copyright 1974 American Mathematical Society
- 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