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Approximating potential integrals by cardinal basis interpolants on multivariate scattered data

✍ Scribed by G. Allasia


Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
981 KB
Volume
43
Category
Article
ISSN
0898-1221

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✦ Synopsis


A

multivariate interpolation operator on scattered data, expressed as a convex combination of cardinal basis functions depending on the inverse (s -2)-power of the Euclidean distance in W (s 2 3) is proposed to give numerical approximations of the integral representing the potential function of the Newtonian field generated by a continuous mass distribution. The operator can be used to interpolate the msss density or directly the potential function, as well as to remap them on a regular grid or a convenient point set. Considerations on the Newtonian potential energy of a system of mass points permit us to introduce quite naturally the operator and to prove some remarkable properties; then the application to the continuous case is considered. Computational performances and possible applications of the operator are outlined.