Abstract
Spherical and harmonic splines are closely related approaches to solve interpolation/approximation as well as boundary value problems on the sphere and on regular (sphere-like) surfaces, respectively. In any case they lead to a system of linear equations which requires fast summation methods for the kernel sums. The fast multipole method achieves just that and is combined in this paper with a preconditioner using the same decomposition of the computational domain to solve the system of linear equations resulting from spherical/harmonic splines. Due to the localizing nature of splines, regional problems can also be treated with this approach.
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Gutting, M. (2013). Fast Spherical/Harmonic Spline Modeling. In: Freeden, W., Nashed, M., Sonar, T. (eds) Handbook of Geomathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27793-1_47-1
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DOI: https://doi.org/10.1007/978-3-642-27793-1_47-1
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