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A Note on the Rate of Convergence of Hermite-Fejér Interpolation Polynomials*

Published online by Cambridge University Press:  20 November 2018

R. B. Saxena
R. B. Saxena*
Affiliation:
University of Alberta, Edmonton, Canada
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The Hermite-Fejér interpolation polynomial Hn[f] of degree ≤2n—1 is defined by

(1)

Where

(2)

are the zeroes of Chebyshev polynomial of first kind Tn(x)=cos n(arc cos x).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 2 , 01 June 1974 , pp. 299 - 301
Copyright
Copyright © Canadian Mathematical Society 1974

Footnotes

*

This research has been supported by the National Research Council Grant NRC-A-3094.

References

1. Bojanic, R., A note on the precision of interpolation by Hermite-Fejér polynomials, Proceedings of the Conference on constructive theory of functions. Akadémiai Kiadό, Budapest (1972), pp. 69-76.Google Scholar
2. Fejér, L., Über Interpolation, Göttinger Nachrichten(1916), pp. 66-91.Google Scholar
3. Kis, O., Remark on the order of convergence of Lagrange interpolation, Annales Univ. Sci., Budapest, 11 (1968), pp. 27-40.Google Scholar
4. Moldvan, E., Observatii aspura unor procedee de inter polare generalizate, Acad. Rep. Pop. Romine, Bui. Stil, Sect. Mat. Fiz. 6 (1954), pp. 472-482 (Romanian, French and Russian summaries).Google Scholar
5. Shisha, O. and Mond, B., The rapidity of convergence of the Hermite-Fejér approximation to functions of one or several variables, Proc. Amer. Math. Soc. (1966), pp. 1269-1276.Google Scholar
6. Vértesi, P. O. H., On the convergence of Hermite-Fejér interpolation, Acta. Math. Acad. Sci. Hungar. 22 (1-2), (1971), pp. 151-158.Google Scholar