Resolution of model-fitting methods

Abstract

Mathematical models of observations may contain non-linearly parametric terms that are very similar. An example is a pair of exponentials whose decay constants differ relatively little. This paper investigates, for a general class of model-fitting methods, how the ability to resolve the pertinent terms from error-corrupted observations depends on the criterion of goodness of fit employed. The results presented include earlier results on a limited class of non-linear least-squares problems as a special case