Modified Versions of Estimates based on Least Squares and Minimum Norm

Abstract

In an up-to-date numerical adjustment method of geodesy, the matrix of coefficients is subjected to spectral analysis and singular value decomposition (SVD). While studying SVD, one comes to the conclusion that there exist matrices which are ill-conditioned with respect to the determination of eigenvalues. This paper proves that the eigenvalues of one class of symmetric matrices occurring in geodesy are well defined, that is, they are less sensitive to slight changes of the elements of the matrix.