Exponential Data Fitting and its Applications

Indexed in: Scopus

Real and complex exponential data fitting is an important activity in many different areas of science and engineering, ranging from Nuclear Magnetic Resonance Spectroscopy and Lattice Quantum ...
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Exponential data fitting

Pp. 1-26 (26)

Victor Pereyra and Godela Scherer

Abstract

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.

Keywords:

Exponential data fitting; separable nonlinear least squares; Prony’s method

Affiliation:

Computational Sciences Research Institute San Diego State University San Diego, CA, USA.