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Remarks on Quasi-Hermite-Fejér Interpolation

Published online by Cambridge University Press:  20 November 2018

A. Sharma
A. Sharma*
Affiliation:
University of Alberta, Calgary
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Let

1

be n+2 distinct points on the real line and let us denote the corresponding real numbers, which are at the moment arbitrary, by

2

The problem of Hermite-Fejér interpolation is to construct the polynomials which take the values (2) at the abscissas (1) and have preassigned derivatives at these points. This idea has recently been exploited in a very interesting manner by P. Szasz [1] who has termed qua si-Hermite-Fejér interpolation to be that process wherein the derivatives are only prescribed at the points x1, x2, …, xn and the points -1, +1 are left out, while the values are prescribed at all the abscissas (1).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 7 , Issue 1 , March 1964 , pp. 101 - 119
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Szász, P., On Quasi - Hermite Fejér Interpolation. Acta Mathematicae Hungaricae, Vol.X (1959) pp.413–439.Google Scholar
2. Fejér, L., Űber Interpolation. Nachrichten der Gesellschaft der Wissen-Grottingen (1916) pp. 66–91.Google Scholar
3. Grűnwald, G., On the Theory of Interpolation. Acta Mathematica Vol. 75 (1943) pp.219–245.Google Scholar
4. Egerváry, andTurán, P., Notes on Interpolation V. Acta Math. Hungaricae, Vol. 9 (1958) pp. 259–267.Google Scholar
5. Szegő, G., Orthogonal Polynomials. American Math. Soc. Colloquium (1939).Google Scholar
6. Egerváry, andTurán, P., Notes on Interpolation VI. Acta Math. Hungaricae, Vol. 10 (1959) pp.55–62.Google Scholar
7. Balázs, J. and Turán, P., Notes on Interpolation VII. Acta Math. Hungaricae, Vol. 10 (1959) pp. 63–68.Google Scholar
8. Erdélyi, A., Higher Transcendental Functions. Vol. 2 (1953).Google Scholar