Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-22T04:38:55.474Z Has data issue: false hasContentIssue false
  • English
  • Français

An Interpolatory Rational Approximation

Published online by Cambridge University Press:  20 November 2018

A. Meir
A. Meir*
Affiliation:
University of Alberta, Edmonton, AlbertaCanada T6G 2G1
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The classical Hermite-Fejér interpolation process is a positive linear mapping from C[-1, 1] into the space of polynomials of degree ≤2n-1. If Tn(x) denotes the Tchebisheff polynomial of degree n and xk = xnk(k = 1,2, …, n) its roots, then for any given f∈ C[-1, 1] the Hermite-Fejér image Hnf of f is defined by

1.1

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 21 , Issue 2 , 01 June 1978 , pp. 197 - 200
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Bojanic, R., A note on the precision of interpolation by Hermite-Fejér polynomials. Proc. Conference on Constructive Theory of Functions, 1969. Akadémiai Kiadó (Budapest, 1972), 69-76.Google Scholar
2. Fejér, L., Über Interpolation. Göttinger Nachrichten (1916), 66-91.Google Scholar
3. Szüsz, P., and Turán, P., On the constructive theory of functions, III. Studia Sci. Math. Hungar. 1 (1966), 315-322.Google Scholar
4. Sharma, A. and Tzimbalario, J., Quasi-Hermite-Fejer Type Interpolation of Higher Order, Journal Approx. Theory 13 (1975), 431-442.Google Scholar