The least-squares solution to the discrete altimetry-gravimetry boundary-value problem for determination of the global gravity model

2005 ◽  
pp. 192-209
Keyword(s):  
Boundary Value Problem ◽  
Least Squares ◽  
Gravity Model ◽  
Boundary Value ◽  
Least Squares Solution ◽  
Global Gravity ◽  
Global Gravity Model

scholarly journals Splitting least squares and collocation procedures for two-point boundary value problems

1985 ◽  
Vol 27 (2) ◽  
pp. 167-193
Author(s):  
John Locker ◽  
P. M. Prenter
Keyword(s):  
Linear System ◽  
Boundary Value Problem ◽  
Numerical Solution ◽  
Least Squares ◽  
Boundary Value ◽  
Linear Operators ◽  
Point Boundary ◽  
System Error ◽  
Densely Defined ◽  
Split System

AbstractLet L, T, S, and R be closed densely defined linear operators from a Hubert space X into X where L can be factored as L = TS + R. The equation Lu = f is equivalent to the linear system Tv + Ru = f and Su = v. If Lu = f is a two-point boundary value problem, numerical solution of the split system admits cruder approximations than the unsplit equations. This paper develops the theory of such splittings together with the theory of the Methods of Least Squares and of Collocation for the split system. Error estimates in both L2 and L∞ norms are obtained for both methods.

scholarly journals The Impact of Noise in a GRACE/GOCE Global Gravity Model on a Local Quasi‐Geoid

2019 ◽  
Vol 124 (3) ◽  
pp. 3219-3237 ◽  
Author(s):  
Cornelis Slobbe ◽  
Roland Klees ◽  
Hassan H. Farahani ◽  
Lennard Huisman ◽  
Bas Alberts ◽  
...  
Keyword(s):  
Gravity Model ◽  
Global Gravity ◽  
The Impact ◽  
Global Gravity Model

scholarly journals Determination of Planetary Masses from the Motions of Comets

1972 ◽  
Vol 45 ◽  
pp. 209-226
Author(s):  
W. J. Klepczynski
Keyword(s):  
Least Squares ◽  
Numerical Integration ◽  
Numerical Experiments ◽  
Close Approach ◽  
Variational Equations ◽  
Orbit Correction ◽  
Partial Derivatives ◽  
Least Squares Solution ◽  
The Masses

A brief survey is given of past determinations of the masses of the principal planets from analyses of the motions of comets. Some numerical experiments using comets which have close approaches to Jupiter are made. As a result of these experiments, it is concluded that the conventional least squares solution for the correction to the mass of Jupiter is inadequate for comets which have a close approach to Jupiter. It is further concluded that perhaps, in some cases, the apparent presence of nongravitational forces is merely a manifestation of the failure of the conventional orbit correction process to adjust correctly the orbits of objects which undergo very large perturbations, and it also may be a consequence of errors in the adopted planetary masses. It is suggested that the use of partial derivatives obtained through the numerical integration of the variational equations may overcome the difficulties.

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