I.6.1: Introduction

We take up the historical developments. Alternating Least Squares was useful for many problems, but it some cases it was not powerful enough to do the job. Or, to put it differently, the subproblems were still too complicated to be efficiently solved a large number of times. In order to solve some additional least squares problems, we can use augmentation. We first illustrate this with some examples.

The examples show that augmentation is somewhat of an art (like integration). The augmentation is in some cases not obvious, and there are no mechanical rules. The idea of adding variables that augment the problem to a simpler one is very general. It is also at the basis, for instance, of the Lagrange multiplier method.