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Mathematical Problems in Engineering
Volume 2012, Article ID 390645, 21 pages
Research Article

Stability Analysis of a Variant of the Prony Method

Escuela de Matemáticas, Universidad Nacional de Colombia, Sede Medellín, Medellín, Colombia

Received 15 June 2012; Accepted 12 October 2012

Academic Editor: Bin Liu

Copyright © 2012 Rodney Jaramillo and Marianela Lentini. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Prony type methods are used in many engineering applications to determine the exponential fit corresponding to a dataset. In this paper we study a variant of Prony's method that was used by Martín-Landrove et al., in a process of segmentation of -weighted MRI brain images. We show the equivalence between that method and the classical Prony method and study the stability of the computed solutions with respect to noise in the data set. In particular, we show that the relative error in the calculation of the exponential fit parameters is linear with respect to noise in the data. Our analysis is based on classical results from linear algebra, matrix computation theory, and the theory of stability for roots of polynomials.