Bibliography: pages 214-220. / The Hilbert space spline theory of Delvos and Schempp, and the reproducing kernel theory of L. Schwartz, provide the conceptual foundation and the construction procedure for rotation-invariant splines on Euclidean spaces, splines on the circle, and splines on the sphere and harmonic outside the sphere. Spherical splines and surface splines such as multi-conic functions, Hardy's multiquadric functions, pseudo-cubic splines, and thin-plate splines, are shown to be largely as effective as least squares collocation in representing geoid heights or gravity anomalies. A pseudo-cubic spline geoid for southern Africa is given, interpolating Doppler-derived geoid heights and astro-geodetic deflections of the vertical. Quadrature rules are derived for the thin-plate spline approximation (over a circular disk, and to a planar approximation) of Stokes's formula, the formulae of Vening Meinesz, and the L₁ vertical gradient operator in the analytical continuation series solution of Molodensky's problem.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:uct/oai:localhost:11427/15821 |
| Date | January 1988 |
| Creators | Van Gysen, Hermanus Gerhardus |
| Contributors | Merry, Charles |
| Publisher | University of Cape Town, Faculty of Engineering and the Built Environment, Division of Geomatics |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Doctoral Thesis, Doctoral, PhD |
| Format | application/pdf |
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