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, Shengxin (2013) On the spectral distribution of kernel matrices related to radial basis functions. Technical Report. Oxford preprint. (Submitted)

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Abstract

This paper focuses on the spectral distribution of kernel matrices related to radial basis functions. By relating a contemporary finite-dimensional linear algebra problem to a classical problem on infinite-dimensional linear integral operator, the paper shows how the spectral distribution of a kernel matrix relates to the smoothness of the underlying kernel function. The asymptotic behaviour of the eigenvalues of a infinite-dimensional kernel operator are studied from a perspective of low rank approximation -- approximating an integral operator in terms of Fourier series or Chebyshev series truncations. Further, we study how the spectral distribution of interpolation matrices of an infinite smooth kernel with 'flat limit' depends on the geometric property of the underlying interpolation points. In particularly, the paper discusses the analytic eigenvalue distribution of Gaussian kernels, which have important application on stable computing of Gaussian radial basis functions.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Integral equations
D - G > Fourier analysis
O - Z > Operator theory
Research Groups:Numerical Analysis Group
ID Code:1701
Deposited By: Lotti Ekert
Deposited On:16 May 2013 07:54
Last Modified:29 May 2015 19:23

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