Splines: Their Equivalence to Collocation
Hans Sünkel
Jan 1984 · Ohio State University, Department of Geodetic Science and Surveying
Ebook
55
Pages
About this ebook
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 Green's 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 Green's 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).
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 ...
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