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Title: Approximation by tranlates of a radial basis function
Authors: Hales, Stephen.
Award date: 2000
Presented at: University of Leicester
Abstract: The aim of this work is to investigate the properties of approximations obtained by translates of radial basis functions. A natural progression in the discussion starts with an iterative refinement scheme using a strictly positive definite inverse multiquadric. Error estimates for this method are greatly simplified if the inverse multiquadric is replaced by a strictly conditionally positive definite polyharmonic spline. Such error analysis is conducted in a native space generated by the Fourier transform of the basis function. This space can be restrictive when using very smooth basis functions. Some instances are discussed where the native space of can be enlarged by creating a strictly positive definite basis function with comparable approximating properties to , but with a significantly different Fourier transform to . Before such a construction is possible however, strictly positive definite functions in d for d < with compact support must be examined in some detail. It is demonstrated that the dimension in which a function is positive definite can be determined from its univariate Fourier transform.;This work is biased towards the computational aspects of interpolation, and the theory is always given with a view to explaining observable phenomena.
Type: Thesis
Level: Doctoral
Qualification: PhD
Rights: Copyright © the author. All rights reserved.
Appears in Collections:Theses, Dept. of Mathematics
Leicester Theses

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