Exponential data fitting
Pp. 1-26 (26)
Victor Pereyra and Godela Scherer
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.
Exponential data fitting; separable nonlinear least squares; Prony’s method
Computational Sciences Research Institute San Diego State University San Diego, CA, USA.