Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-26T01:00:41.254Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

REFERENCES

1.Gantmacher, R., Matrix Theory II (Chelsea Publications, N.Y., 1964).Google Scholar
2.Goodman, T. N. T. and Lee, S. L., B-splines on the circle and trigonometric B-splines, in Approximation Theory and Spline Functions (Eds. Singh, S. P., Burry, J. W. H. and Watson, B.), D. Riedel Pub. Co., Holland 1983, 297–325.Google Scholar
3.Kis, O., Remarks on interpolation (Russian), Acta Math. Acad. Sci. Hangar. 11 (1960), 49–64.Google Scholar
4.Lorentz, G. G., Jetter, K. and Riemenschneider, S., Birkhoff interpolation, in Endycopedia of Math. 19 (Addison-Wesley, Reading, MA 1983).Google Scholar
5.Lorentz, G. G., Approximation of functions (Chelsea Publications, N.Y. 1986).Google Scholar
6.Sharma, A. and Varga, R. S., On a particular 2-periodic lacunary trigonometric interpolation problem on equidistant nodes, Results in Mathematics 16 (1989), 333–404.Google Scholar
7.Sharma, A., Szabados, J. and Varga, R. S., 2-periodic lacunary trigonometric interpolation: the (0, M) cases, Constructive Theory of Functions '87 (House of Bulgar, Acad. Sciences Sofia 1988), 420–427.Google Scholar
8.Sharma, A. and Saxena, R. B., Almost Hermitian trigonometric interpolation in three equidistant nodes, Aequationes Math. 41 (1991), 55–69.Google Scholar
9.Sharma, A., Szabados, J. and Varga, R. S., Some two periodic trigonometric interpolation problems on equidistant nodes, Analysis, to appear.Google Scholar
10.Timan, A. F., Theory of Approximation of Functions of a Real Variable (English translation), (Hindustan Pub. Co., Delhi-7, 1986).Google Scholar