Application of Eigenvalue Decomposition in the Parallel Computation of a CHAMP 100x100 Gravity Field

To obtain an alternative gravity solution to that of EIGEN1S, the author's Singular Value Decomposition(SVD) tool,

P

arallel

LA

rge

S

vd

S

olver (PLASS), was applied to the CHAMP normal matrix

ngl-eigen-1s

{xc[2]} to perform an Eigenvalue Decomposition (EVD) analysis. The EIGEN1S solution is based on the Tikhonov regularization method of approximating the ill-conditioned system of equations in a subspace of lower rank. In the EVD solution, poorly determined linear combinations of parameter corrections are removed in the culpable eigenspace of the unconstrained least-squares normal equation. The selection of eigenvalues to be removed, is based upon a new method and four different common optimization (truncation) criteria. The new method, the Kaula Eigenvalue (KEV) relation, optimizes the removal of eigenvalues to best satisfy Kaula's Rule. The four other techniques are: inspection, relative error, norm-norm minimization, and finding the minimum trace of the mean square error (MSE) matrix. Analysis of the five different EVD gravity fields was performed. Two of them were shown to be comparable to the EIGEN1S CHAMP solution obtained by the GeoForschungsZentrum Potsdam (GFZ) {xc[2]}. The best of the five optimal solutions, that of the KEV, is presented. The number of estimated parameters is 11216.