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 finitedimensional linear algebra problem to a classical problem on infinitedimensional 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 infinitedimensional 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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