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A modified Prony algorithm for fitting functions defined by difference equations. (English) Zbl 0723.65006
The aim of this paper is to reformulate, to generalize and to investigate the stability of the modified Prony algorithm introduced by the first author [SIAM J. Numer. Analysis 12, 571-592 (1975; Zbl 0322.65007)], with special reference to rational and exponential fitting. The algorithm, originally for exponential functions, is generalized to the least squares fitting of any function which satisfies a linear homogeneous difference equation. Details of the implementation of the algorithm are given. A test problem is presented and simulation study compares the modified Prony algorithm with the Levenberg algorithm.

65D10Smoothing, curve fitting
65C99Probabilistic methods, simulation and stochastic differential equations (numerical analysis)
62J02General nonlinear regression
65J15Equations with nonlinear operators (numerical methods)
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