Exponential data fitting

In this initial chapter we consider some of the basic methods used in the fitting of data by real and complex linear combinations of exponentials. We have selected the classes of methods that are most frequently used in many different fields: variable projections for solving this separable nonlinear least squares problem, derivatives and variants of Prony’s method, which rely on evenly sampled data and take special advantage of the particular form of the approximation and finally the matrix-pencil method. We also have implemented some of these techniques and compared them in a few examples to support some comments on their advantages and disadvantages and exemplify their performance in terms of computing time and robustness, specially considering that this is a notoriously ill-conditioned problem in many cases.