A Survey on Spherical Spline

Spline functions that approximate data given on the sphere are developed in a weighted Sobolev space setting. The exibility 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 pseudodiierential equations.

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