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Mon, 03 Apr 2000 00:00:00 +0200Mon, 03 Apr 2000 00:00:00 +0200A Survey on Spherical Spline Approximation
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/590
Spline functions that approximate data given on the sphere are developed in a weighted Sobolev space setting. The flexibility of the weights makes possible the choice of the approximating function in a way which emphasizes attributes desirable for the particular application area. Examples show that certain choices of the weight sequences yield known methods. A convergence theorem containing explicit constants yields a usable error bound. Our survey ends with the discussion of spherical splines in geodetically relevant pseudodifferential equations.Willi Freeden; Michael Schreiner; R. Frankepreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/590Mon, 03 Apr 2000 00:00:00 +0200Generalized Weighted Spline Approximation on the Sphere
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/737
Spline functions that interpolate data given on the sphere are developed in a weighted Sobolev space setting. The flexibility of the weights makes possible the choice of the approximating function in a way which emphasizes attributes desirable for the particular application area. Examples show that certain choices of the weight sequences yield known methods. A pointwise convergence theorem containing explicit constants yields a useable error bound.Willi Freeden; R. Frankepreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/737Mon, 03 Apr 2000 00:00:00 +0200