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On Lagrange interpolation with equidistant nodes

Published online by Cambridge University Press:  17 April 2009

Graeme J. Byrne ,
T.M. Mills  and
Simon J. Smith
Graeme J. Byrne
Affiliation:
Department of Mathematics, Bendigo College of Advanced Education, PO Box 199 Bendigo Vic 3550, Australia
T.M. Mills
Affiliation:
Department of Mathematics, Bendigo College of Advanced Education, PO Box 199 Bendigo Vic 3550, Australia
Simon J. Smith
Affiliation:
Department of Mathematics, Bendigo College of Advanced Education, PO Box 199 Bendigo Vic 3550, Australia
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Abstract

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A quantitative version of a classical result of S.N. Bernstein concerning the divergence of Lagrange interpolation polynomials based on equidistant nodes is presented. The proof is motivated by the results of numerical computations.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 42 , Issue 1 , August 1990 , pp. 81 - 89
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Berman, D.L., ‘Divergence of the Hermite-Fejér interpolation process’, (in Russian), Uspehi Mat. Nauk. 13 (1958), 143–148.Google Scholar
[2]Bernstein, Serge, ‘Quelques remarques sur l'interpolation’, Math. Ann. 79 (1918), 1–12.CrossRefGoogle Scholar
[3]Luke, Yudell L., The special functions and their approximations, Vol. I (Academic Press, New York, 1969).Google Scholar
[4]Natanson, I.P., Constructive function theory, Vol. III (Frederick Ungar, New York, 1965).Google Scholar
[5]Runck, Paul Otto, ‘Über Konvergenzfragen bei Polynominterpolation mit äquidistanten Knoten I.’, J. Reine Angew. Math. 208 (1961), 51–69.CrossRefGoogle Scholar
[6]Runck, Paul Otto, ‘Über Konvergenzfragen bei Polynominterpolation mit äquidistanten Knoten II.’, J. Reine Angew. Math. 210 (1962), 175–204.CrossRefGoogle Scholar
[7]Whittaker, E.T. and Watson, G.N., A course of modern analysis, Fourth edition (Cambridge Univ. Press, London, 1973).Google Scholar