Approximating potential integrals by cardinal basis interpolants on multivariate scattered data
type: Item
instance of: scholarly article
title: Approximating potential integrals by cardinal basis interpolants on multivariate scattered data
zbMATH Open document ID: 1006.65011
DOI: 10.1016/S0898-1221(01)00286-3
publication date: 2002-08-15T00:00:00Z
review text: The paper is concerned with the numerical approximation of the integral representation the potential function of the Newtonian field generated by a continuous mass distribution \[ u(x)= {1\over s- 2} \int_V {\mu(u)\over d^{s- 2}(x, u)} du,\quad s= 3,4,\dots, \] where \(d(\cdot,\cdot)\) denotes the Euclidean distance. The proposed approximations are based on the multivariate interpolation operator \[ \Phi(x; f,\Delta_n)= \sum^n_{j=1} f(x_j) {\prod^n_{\substack{ k=1\\ k\neq j}} d^{s-2}(x, x_k)\over \sum^n_{i=1} \prod^n_{\substack{ k=1\\ k\neq i}} d^{s-2}(x, x_k)}= \sum^n_{j=1} f(x_j) {1/d^{s- 2}(x, x_j)\over \sum^n_{i=1} (1/d^{s-2}(x, x_i))}, \] where \(\Delta_n:= \{x_1,\dots, x_n\}\). The authors prove some properties of the operator and propose some computational performances. Numerical tests are postponed to a forthcoming paper.
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 41A63
Mathematics Subject Classification ID: 31B10
Mathematics Subject Classification ID: 41A05
zbMATH DE Number: 1781502
zbMATH Keywords: multivariate interpolation
zbMATH Keywords: potential integrals
zbMATH Keywords: cardinal basis
zbMATH Keywords: scattered data
author: Giampietro Allasia
reviewed by: Gabriele Steidl
describes a project that uses: QSHEP3D
MaRDI profile type: Publication
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 1781502