Premium
Spline methods in geodetic approximation problems
Author(s) -
Freeden Willi,
Törnig W.
Publication year - 1982
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670040124
Subject(s) - mathematics , thin plate spline , spline (mechanical) , spline interpolation , hilbert space , smoothing spline , mathematical analysis , geodetic datum , reproducing kernel hilbert space , smoothing , ellipsoid , hermite spline , geoid , norm (philosophy) , bilinear interpolation , geodesy , statistics , structural engineering , geophysics , political science , law , geography , engineering , geology , measured depth
This paper is concerned with spline methods in a reproducing kernel Hilbert space consisting of functions defined and harmonic in the outer space of a regular surface (e.g. sphere, ellipsoid, telluroid, geoid, (regularized) earth's surface). Spline methods are used to solve interpolation and smoothing problems with respect to a (fundamental) system of linear functional giving information about earth's gravity field. Best approximations to linear functionals are discussed. The spline of interpolation is characterized as the spline of best approximation in the sense of an appropriate (energy) norm.