On spectral distribution of kernel matrices related to radial basis functions
type: Item
instance of: scholarly article
title: On spectral distribution of kernel matrices related to radial basis functions
zbMATH Open document ID: 1356.45001
published in: Numerical Algorithms
publication date: 2016-01-25T00:00:00Z
review text: The paper shows an involvement of spectral distribution of kernel matrices related to radial basis functions. The paper, further, succeeds in explaining the relation between spectral distribution of a kernel matrix and the smoothness of the underlying kernel function. Main investigation of this paper is to establish a relation between radial basis functions interpolation scheme to the discrete integral equation of the first kind. Investigation of the corresponding classical infinite-dimensional linear operator problem replaces consideration of the finite-dimensional linear algebra problem. Theorems 4 and 5 show as how the decay of eigenvalues of kernel matrices of radial basis functions is closely related to the smoothness of the concerned radial basis functions. The claim (candid) is that though the results found in the literature may show connections with the linear integral equations, yet none of them belongs to the community of the radial basis functions, which this paper contains. The connectivity between the radial basis functions interpolation problem and the Fredholm integral equation of the first kind is presented exclusively, and simultaneously, the Weyl-Courant minimax principle (besides other relevant lemmas) is introduced. While main results are given in Section 3, the discussion in Section 4 attracts the potentiality of the results of the present paper.
reviewed by: Deshna Loonker
Mathematics Subject Classification ID: 45C05
Mathematics Subject Classification ID: 45B05
Mathematics Subject Classification ID: 47A52
Mathematics Subject Classification ID: 47A75
zbMATH DE Number: 6535406
zbMATH Keywords: spectral distribution
zbMATH Keywords: eigenvalues
zbMATH Keywords: radial basis function
zbMATH Keywords: Fredholm integral equation
zbMATH Keywords: Weyl-Coutant minimax principle
author: A. J. Wathen
author: Sheng-Xin Zhu
describes a project that uses: rbf_qr
MaRDI profile type: Publication
OpenAlex ID: W2172067320
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DOI: 10.1007/S11075-015-9970-0
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description: scientific article; zbMATH DE number 6535406