Boundary integral equations on the sphere with radial basis functions: Error analysis
type: Item
instance of: scholarly article
title: Boundary integral equations on the sphere with radial basis functions: Error analysis
zbMATH Open document ID: 1176.65147
author: N. E. Zubov
published in: Applied Numerical Mathematics
publication date: 2009-09-28T00:00:00Z
review text: The authors present the boundary integral equations on the sphere with radial basis functions. They first introduce the integral formulation of the boundary value problems into boundary integral equations. Later they discuss the use of radial basis functions to define the subspace used in the approximation. The approximation property in different Sobelev norms of the subspace are presented. Convergence of the approximation scheme is proved. Numerical experiments are given to support the presented theoretical results.
reviewed by: Seenith Sivasundaram
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 5608063
zbMATH Keywords: boundary integral equation
zbMATH Keywords: sphere
zbMATH Keywords: radial basis function
zbMATH Keywords: spherical basis function
zbMATH Keywords: numerical experiments
MaRDI profile type: Publication
full work available at URL: j.apnum.2008.12.033
OpenAlex ID: W1969287581
cites work: Q4112938
cites work: A necessary and sufficient condition for strictly positive definite functions on spheres
cites work: Optimal lower bounds for cubature error on the sphere \(S^2\)
cites work: Linear integral equations.
cites work: Continuous and discrete least-squares approximation by radial basis functions on spheres
cites work: Q4953888
cites work: Spherical harmonics
cites work: Scattered Data Interpolation on Spheres: Error Estimates and Locally Supported Basis Functions
cites work: Distributing many points on a sphere
cites work: Improved error bounds for scattered data interpolation by radial basis functions
cites work: Positive definite functions on spheres
cites work: Approximation on the sphere using radial basis functions plus polynomials
cites work: Scattered Data Approximation
cites work: Strictly Positive Definite Functions on Spheres
DOI: 10.1016/J.APNUM.2008.12.033
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description: scientific article; zbMATH DE number 5608063