SPLINES. Their Equivalence to Collocation,
OHIO STATE UNIV COLUMBUS DEPT OF GEODETIC SCIENCE AND SURVEYING
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The application of splines in geodesy was mainly restricted to the solution of one-dimensional problems like interpolation, differentiation, approximation, solution of differential equations, etc. Two-dimensional splines turned out to be an adequate tool for the representation of smooth surfaces based on grided data. The purpose of this paper is to present splines on the real line, on the circle, on the sphere, and on the two-dimensional plane in a common and simple framework The Greens function and the frequency domain method. Splines of arbitrary degree, no matter what their domain of definition is, are shown to be recursively related to each other by convolutions of Greens functions. The close relation and little difference, if any between spline and collocation solutions is demonstrated. Additional keywords Fourier transformation Hankel transform Spherical harmonics. Author.
- Numerical Mathematics