Using data with models - Ill-posed problems

An attempt is made to show that the combination of data with models leads to a sequence of conventionally ill-posed problems which can be treated in a systematic and practical way by control-theory techniques. The illustrative approach is to exploit the very great mathematical simplifications which result when the methods of finite dimensional vector spaces are used, thus reducing a lot of difficult mathematics to classical least squares. The immediate motivation for this study comes from ocean acoustic tomography.