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Estimation of parameters in nonlinear problems

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Abstract

In this paper, we describe two efficient methods to estimate parameters in nonlinear least squares problems: continuation and sentinels methods. When the studied system is modeled by differential equations, we have to identify both unknown parameters and initial conditions. For that, we propose to process in two steps: first identify the unknown parameters, then identify again using the found results, considering now both the parameters and the initial conditions as unknown.

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References

  1. Y. Bard, Nonlinear Parameter Estimation (Academic Press, New York, 1974).

    Google Scholar 

  2. M. Benson, Parameter fitting in dynamic models, Ecol. Mod. 6 (1979) 97.

    Article  Google Scholar 

  3. N. De Villiers and D. Glasser, A continuation method for nonlinear regression, SIAM J. Numer. Anal. 18 (1981) 1139.

    Article  MATH  MathSciNet  Google Scholar 

  4. E.J. Doedel and J.P. Kernévez, AUTO: software for continuation and bifurcation problems in ordinary differential equations, Applied Mathematics Report, California Institute of Technology (1986).

  5. L. Kaufman, G.S. Sylvester and M.H. Wright, Structured linear least squares problems in system identification and separable nonlinear data fitting, SIAM J. Optim. 4(4) (1994) 847.

    Article  MATH  MathSciNet  Google Scholar 

  6. J.P. Kernévez, The Sentinel Method and its Application to Environmental Pollution Problems (CRC Press, New York, 1997).

    Google Scholar 

  7. J.L. Lions, Sentinelles pour les Systèmes Distribués (Masson, Paris, 1992).

    Google Scholar 

  8. D.W. Marquardt, An algorithm for least squares estimation of nonlinear parameters, SIAM J. Appl. Math. 11 (1963) 431.

    Article  MATH  MathSciNet  Google Scholar 

  9. D.E. Salane, A continuation approach for solving large residual nonlinear least squares problems, SIAM J. Sci. Statist. Comput. 8(4) (1987) 655.

    Article  MATH  MathSciNet  Google Scholar 

  10. J.M. Varah, A spline least squares method for numerical parameter estimation in differential equations, SIAM J. Sci. Statist. Comput. 3(1) (1982) 28.

    Article  MATH  MathSciNet  Google Scholar 

  11. J.M. Varah, Relative sizes of the Hessian terms in nonlinear estimation, SIAM J. Sci. Statist. Comput. 11(1) (1990) 174.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Institut d'Electronique, Université de Constantine, Route de Aïn-El-Bey, 25000, Constantine, Algeria

    N. Mansouri

  2. Université de Technologie de Compiègne, BP 20529, F-60205, Compiègne Cedex, France

    J.P Kernévez

Authors
  1. N. Mansouri
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  2. J.P Kernévez
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Mansouri, N., Kernévez, J. Estimation of parameters in nonlinear problems. Numerical Algorithms 17, 333–343 (1998). https://doi.org/10.1023/A:1016692609467

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