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An algorithm for exponential fitting revisited

Published online by Cambridge University Press:  14 July 2016

M. R. Osborne  and
G. K. Smyth
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Abstract

An algorithm for exponential fitting is presented which exploits the separable regression structure and a reparametrization. The algorithm has proved very satisfactory, and theoretical reasons for this are developed.

Keywords

PRONY'S METHODSEPARABLE REGRESSIONNON-LINEAR LEAST SQUARESGAUSS–NEWTON ALGORITHMREPARAMETRIZATIONNON-LINEAR EIGENPROBLEM
Type
Part 7—Algorithms and Computations
Information
Journal of Applied Probability , Volume 23 , Issue A: Essays in Time Series and Allied Processes , 1986 , pp. 419 - 430
Copyright
Copyright © 1986 Applied Probability Trust 

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References

Golub, G. H. and Pereyra, V. (1973) The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate. SIAM J. Numer. Anal. 10, 413–432.Google Scholar
Jennrich, R. I. (1969) Asymptotic properties of non-linear least squares estimators. Ann. Math. Statist. 40, 633–643.CrossRefGoogle Scholar
Osborne, M. R. (1975) Some special nonlinear least squares problems. SIAM J. Numer. Anal. 12, 571–592.CrossRefGoogle Scholar
Osborne, M. R. (1976) Nonlinear least squares–the Levenberg algorithm revisited J. Austral. Math. Soc. B 19, 343–357.CrossRefGoogle Scholar
Richards, F. S. G. (1961) A method of maximum-likelihood estimation. J. R. Statist. Soc. B 23, 469–475.Google Scholar
Smyth, G. K. (1985) Separable Parameters and Coupled Iterations in Nonlinear Estimation, Ph.D. Thesis, Australian National University, Canberra.Google Scholar
Wilson, S. R. (1983) Benchmark data sets for the flexible evaluation of statistical software. Computational Statistics and Data Analysis 1, 29–39.Google Scholar