On spectral distribution of kernel matrices related to radial basis functions
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.
scientific article; zbMATH DE number 6535406
scientific article