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A modified Prony algorithm for exponential function fitting. (English) Zbl 0812.62070
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.

62J02General nonlinear regression
65C99Probabilistic methods, simulation and stochastic differential equations (numerical analysis)
65D10Smoothing, curve fitting
65F15Eigenvalues, eigenvectors (numerical linear algebra)
65L99Numerical methods for ODE