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Spectral convergence of multiquadric interpolation

Published online by Cambridge University Press:  20 January 2009

Martin Buhmann  and
Nira Dyn
Martin Buhmann
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 9EW, England
Nira Dyn
Affiliation:
Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel
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Abstract

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In this paper, we consider interpolants on h·ℤn from the closure of the space spanned by translates of the function (‖·‖2 + 1)β/2 (β>−n and not an even nonnegative integer) along h·ℤn. We show that these interpolants approximate a function, whose Fourier transform satisfies certain asymptotic conditions, up to an error of order hp, on any compact domain in ℝn, where p is only restricted by the smoothness of the function.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 36 , Issue 2 , June 1993 , pp. 319 - 333
Copyright
Copyright © Edinburgh Mathematical Society 1993

References

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