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On spherical spline interpolation and approximation
Author(s) -
Freeden W.,
Törnig W.
Publication year - 1981
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670030139
Subject(s) - mathematics , unit sphere , spline (mechanical) , polyharmonic spline , smoothing spline , thin plate spline , mathematical analysis , spherical harmonics , box spline , interpolation (computer graphics) , spline interpolation , smoothing , animation , statistics , computer graphics (images) , structural engineering , computer science , bilinear interpolation , engineering
Spherical spline functions are introduced by use of Green's surface functions with respect to the (Laplace‐)Beltrami operator of the (unit) sphere. Natural (spherical) spline functions are used to interpolate data discretely given on the sphere. A method is presented that allows the smoothing of irregularities in measured values or experimental data. Extensions of Peano's theorem and Sard's theory of best approximation to the spherical case are given by integral formulas. Schoenberg's theorem is transcribed into spherical nomenclature.