Spectral Analysis for Radial Basis Function Collocation Matrices

R. Cavoretto (), A. De Rossi (), M. Donatelli () and S. Serra-Capizzano ()
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R. Cavoretto: Università di Torino, Dipartimento di Matematica
A. De Rossi: Università di Torino, Dipartimento di Matematica
M. Donatelli: Università dell’Insubria – Sede di Como, Dipartimento di Fisica e Matematica
S. Serra-Capizzano: Università dell’Insubria – Sede di Como, Dipartimento di Fisica e Matematica

A chapter in Numerical Mathematics and Advanced Applications 2009, 2010, pp 237-244 from Springer

Abstract: Abstract The aim of this paper is to provide tools and results for the analysis of the linear systems arising from radial basis function (RBF) approximations of partial differential equations (PDEs), see e.g., [1,9]. Informally, a radial function $$\phi (x) : \mathbb{R}^n \rightarrow \mathbb{R} $$ is a function of the Euclidean norm $$\|x\|$$ of x, i.e., $$\phi (x) = \eta (\| x\|) $$ , for $$ \eta (t) : \mathbb{R}^n \rightarrow \mathbb{R}$$

Keywords: Radial Basis Function; Spectral Distribution; Distribution Result; Toeplitz Matrix; Toeplitz Matrice (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/978-3-642-11795-4_24

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