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Hermite Interpolation with Radial Basis Functions on Spheres
 Adv. Comput. Math
, 1999
"... . We show how conditionally negative definite functions on spheres coupled with strictly completely monotone functions (or functions whose derivative is strictly completely monotone) can be used for Hermite interpolation. The classes of functions thus obtained have the advantage over the strictly po ..."
Abstract

Cited by 7 (1 self)
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. We show how conditionally negative definite functions on spheres coupled with strictly completely monotone functions (or functions whose derivative is strictly completely monotone) can be used for Hermite interpolation. The classes of functions thus obtained have the advantage over the strictly positive definite functions studied in [17] that closed form representations (as opposed to series expansions) are readily available. Furthermore, our functions include the historically significant spherical multiquadrics. Numerical results are also presented. AMS classification: 41A05, 41A63, 42A82. Key words and phrases: Spherical interpolation, Hermite interpolation, Radial basis functions. 1. Introduction In 1975 R. Hardy mentioned the possibility of using multiquadric basis functions for Hermite interpolation (see [10], or the survey paper [11]). This problem, however, was not further investigated until the paper [29] by Wu appeared. Since then, the interest in this topic seems to have ...
1.1 History and Outline
"... Originally, the motivation for the basic meshfree approximation methods (radial basis functions and moving least squares methods) came from applications in geodesy, geophysics, mapping, or meteorology. Later, applications were found in many areas such ..."
Abstract
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Originally, the motivation for the basic meshfree approximation methods (radial basis functions and moving least squares methods) came from applications in geodesy, geophysics, mapping, or meteorology. Later, applications were found in many areas such