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On Hermite-Fejér type interpolation on the Chebyshev 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, La Trobe University College of Northern Victoria, PO Box 1999 Bendigo Vic 3550, Australia
T.M. Mills
Affiliation:
Department of Mathematics, La Trobe University College of Northern Victoria, PO Box 1999 Bendigo Vic 3550, Australia
Simon J. Smith
Affiliation:
Department of Mathematics, La Trobe University College of Northern Victoria, PO Box 1999 Bendigo Vic 3550, Australia
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Abstract

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Given f ∈ C [−1, 1], let Hn, 3(f, x) denote the (0,1,2) Hermite-Fejér interpolation polynomial of f based on the Chebyshev nodes. In this paper we develop a precise estimate for the magnitude of the approximation error |Hn, 3(f, x) − f(x)|. Further, we demonstrate a method of combining the divergent Lagrange and (0,1,2) interpolation methods on the Chebyshev nodes to obtain a convergent rational interpolatory process.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 47 , Issue 1 , February 1993 , pp. 13 - 24
Copyright
Copyright © Australian Mathematical Society 1993

References

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