Tensor structure applied to the leastsquares method, revisited
Abstract
The geometrical approach to the leastsquares, based on differential geometry with tensor structure and notations, describes the adjustment theory in a simple and plausible manner. The development relies heavily on orthonormal space and surface vectors, and on the extrinsic properties of surfaces linking the two kinds of vectors. In order to relate geometry to adjustments, the geometrical concepts are extended to an ndimensional space and u or rdimensional surfaces, where n is the number of observations, u is the number of parameters in the parametric method and r is the number of conditions in the condition method, with n=u+r. Connection is made to Hilbert spaces by demonstrating that the tensor approach to the leastsquares is a classical case of the Hilbertspace approach.
 Publication:

Bulletin Geodesique
 Pub Date:
 March 1984
 DOI:
 10.1007/BF02521753
 Bibcode:
 1984BGeod..58....1B