SPLINES. Their Equivalence to Collocation,
Abstract
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).
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1984
- Accession Number
- ADA155250
Entities
People
- H. Sonkel
Organizations
- Ohio State University