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Zbl 0812.62070
Osborne, M.R.; Smyth, G.K.
A modified Prony algorithm for exponential function fitting. (English)
[J] SIAM J. Sci. Comput. 16, No.1, 119-138 (1995). ISSN 1064-8275; ISSN 1095-7197/e

Summary: A modification of the classical technique of Prony for fitting sums of exponential functions to data is considered. The method maximizes the likelihood for the problem (unlike the usual implementation of Prony's method, which is not even consistent for transient signals), proves to be remarkably effective in practice, and is supported by an asymptotic stability result. Novel features include a discussion of the problem parametrization and its implications for consistency. The asymptotic convergence proofs are made possible by an expression for the algorithm in terms of circulant divided difference operators.

MSC 2000:: *62J02 General nonlinear regression
65C99 Numerical simulation
65D10 Smoothing
65F15 Eigenvalues (numerical linear algebra)
65L99 Numerical methods for ODE

Keywords: Pisarenko's method; nonlinear least squares; inverse iteration; Levenberg algorithm; circulant matrices; maximum likelihood; fitting sums of exponential functions; Prony's method; asymptotic stability result; parametrization; consistency; asymptotic convergence; circulant divided difference operators

Cited in: Zbl 0833.62087

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