On the identity of two solution algorithms of the ‘improved normalized squared differences’ matrix adjustment model

Abstract

The paper is a supplement for an article recently published in this journal. That paper proved that if the sign-preservation requirement is dropped then the solution of the so-called improved normalized squared differences (INSD) two-directional matrix adjustment model is the same as the result of the ‘additive correction iteration algorithm’ which the author has been using successfully for decades. It also argued that if the sign-preservation requirement is dropped then the iteration procedure suggested by the authors of the INSD-model boils down to the same algorithm. Since the formal proof of this statement was not available at the time, in this paper the author duly publishes the three-and-a-half pages long proof he elaborated. In the conclusion the merit of this and similar, yet barely rigorously analysed iteration algorithms and the possible useful extensions are also outlined.