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Trigonometric interpolation*

Published online by Cambridge University Press:  20 January 2009

T. N. T. Goodman  and
A. Sharma
T. N. T. Goodman
Affiliation:
University of DundeeDundee DD1 4HNScotland
A. Sharma
Affiliation:
University of AlbertaEdmonton, AlbertaCanada
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Abstract

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We consider interpolation at 2n equidistant nodes in [0,π) from the space ℱN spanned by sines and cosines of odd multiples of x. This interpolation problem is shown to be correct for an arbitrary sequence of derivatives specified at all the nodes. Explicit expressions for the fundamental polynomials are obtained and it is shown that under mild smoothness assumptions on the function f interpolant from ℱN converges uniformly to f as the node spacing goes to zero.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 35 , Issue 3 , October 1992 , pp. 457 - 472
Copyright
Copyright © Edinburgh Mathematical Society 1992

References

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