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Modified multiquadric methods for scattered data interpolation over a sphere. (English) Zbl 0714.65010
The aim of this paper is to present the problem of constructing a smooth function defined over the sphere which interpolates the given data. Several methods which are appropriate modifications of R. L. Hardy’s planar multiquadric method [Multiquadric equations of topography and other irregular surfaces.J. Geophys. Res. 76, 1905-1915 (1971)] are presented, compared and discussed: the restriction of trivariate multiquadric interpolation to the sphere, spherical multiquadric interpolation due to R. L. Hardy and W. M. Goepfert [Least squares prediction of gravity anomalies, gesidal undulations, and deflections of the vertical with multiquadric harmonic functions. Geophys. Res. Lett. 2, 423-426 (1975)] and a scheme called: ‘elliptic multiquadric interpolation’.
Reviewer: M.Gaşpar (Iaşi)

MSC:
65D05 Numerical interpolation
65D10 Numerical smoothing, curve fitting
86A30 Geodesy, mapping problems
86A10 Meteorology and atmospheric physics
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