The Mathematical Institute, University of Oxford, Eprints Archive

On the spectral distribution of kernel matrices related to
radial basis functions

Wathen, A. J. and Zhu, S.-X. (2012) On the spectral distribution of kernel matrices related to
radial basis functions.
Numerische Mathematik . (Submitted)

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Abstract

This paper focuses on the spectral distribution of kernel matrices related to radial basis functions. The asymptotic behaviour of eigenvalues of kernel matrices related to radial basis functions with different smoothness are studied. These results are obtained by estimated the coefficients of an orthogonal expansion of the underlying kernel function. Beside many other results, we prove that there are exactly (k+d−1/d-1) eigenvalues in the same order for analytic separable kernel functions like the Gaussian in Rd. This gives theoretical support for how to choose the diagonal scaling matrix in the RBF-QR method (Fornberg et al, SIAM J. Sci. Comput. (33), 2011) which can stably compute Gaussian radial basis function interpolants.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:1630
Deposited By:Peter Hudston
Deposited On:24 Nov 2012 08:59
Last Modified:24 Nov 2012 08:59

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