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Iterative sparse interpolation in reproducing kernel Hilbert spaces

Dodd, T.J. and Harrison, R.F. (2001) Iterative sparse interpolation in reproducing kernel Hilbert spaces. Research Report. ACSE Research Report no. 814 . Automatic Control and Systems Engineering, University of Sheffield

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Abstract

The problem of interpolating data in reproducing kernel Hilbert spaces is well known to be ill-conditioned. In the presence of noise, regularisation can be applied to find a good solution. In the noise-free case, regularisation has the effect of over-smoothing the function and few data points are interpolated. In this paper an alternative framework, based on sparsity, is proposed for interpolation of noise-free data. Iterative construction of a sparse sequence of interpolants is shown to be well defined and produces good results.

Item Type: Monograph (Research Report)
Copyright, Publisher and Additional Information: The Department of Automatic Control and Systems Engineering research reports offer a forum for the research output of the academic staff and research students of the Department at the University of Sheffield. Papers are reviewed for quality and presentation by a departmental editor. However, the contents and opinions expressed remain the responsibility of the authors. Some papers in the series may have been subsequently published elsewhere and you are advised to cite the later published version in these instances.
Institution: The University of Sheffield
Academic Units: The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Automatic Control and Systems Engineering (Sheffield) > ACSE Research Reports
The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Automatic Control and Systems Engineering (Sheffield)
Depositing User: Miss Anthea Tucker
Date Deposited: 25 Jul 2012 09:38
Last Modified: 07 Jun 2014 10:17
Status: Published
Publisher: Automatic Control and Systems Engineering, University of Sheffield
URI: http://eprints.whiterose.ac.uk/id/eprint/74447

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