Advanced Physical Geodesy |
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Page 94
Helmut Moritz. as a linear combination of q " base functions " If the kernel function K ( P , Q ) the base functions ( P ) . i has a simple analytical expression , then i • 2 ( P ) = L & K ( P , Q ) ( 12-12 ) will also be simple ...
Helmut Moritz. as a linear combination of q " base functions " If the kernel function K ( P , Q ) the base functions ( P ) . i has a simple analytical expression , then i • 2 ( P ) = L & K ( P , Q ) ( 12-12 ) will also be simple ...
Page 196
Helmut Moritz. 24. HILBERT SPACES WITH KERNEL FUNCTIONS A deeper mathematical understanding of least - squares collocation re- quires the theory of Hilbert spaces that possess a kernel function . There- fore we shall in this section ...
Helmut Moritz. 24. HILBERT SPACES WITH KERNEL FUNCTIONS A deeper mathematical understanding of least - squares collocation re- quires the theory of Hilbert spaces that possess a kernel function . There- fore we shall in this section ...
Page 197
Helmut Moritz. 24. HILBERT SPACES WITH KERNEL FUNCTIONS A deeper mathematical understanding of least - squares collocation re- quires the theory of Hilbert spaces that possess a kernel function . There- fore we shall in this section ...
Helmut Moritz. 24. HILBERT SPACES WITH KERNEL FUNCTIONS A deeper mathematical understanding of least - squares collocation re- quires the theory of Hilbert spaces that possess a kernel function . There- fore we shall in this section ...
Contents
PART A GENERAL BACKGROUND | 1 |
The Earths Gravity Field | 2 |
Reference Ellipsoid and Anomalous Gravity Field | 7 |
Copyright | |
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analytical continuation anomalous potential base functions basic boundary condition boundary-value problem coefficients compute considered convergence corresponding covariance function covariance matrix defined denotes derivative differential earth's surface elements estimate expressed fact formula function K(P,Q geodetic geoid geometrical given grad gradient gravitational field gravitational potential gravity anomalies gravity space gravity vector harmonic function Heiskanen and Moritz Hilbert space Hölder condition infinite inner product integral inverse kernel function Laplace's equation least-squares collocation linear functional mathematical means measurements minimum Molodens Molodensky's problem nm nm nm nonlinear norm normal gravity notation observations obtained operator parameters physical geodesy probability space quantities radius random real number reference ellipsoid Runge's theorem satisfied signal solution spherical harmonics spherical-harmonic statistical stochastic process Stokes telluroid theorem tion transformation Tscherning unit sphere variance zero ах