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Numerical Analysis pp 105–116Cite as

The Levenberg-Marquardt algorithm: Implementation and theory

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 630))

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References

  1. Bard, Y. [1970]. Comparison of gradient methods for the solution of nonlinear parameter estimation problem, SIAM J. Numer. Anal. 7, 157–186.

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  2. Brown, K. M. and Dennis, J. E. [1971]. New computational algorithms for minimizing a sum of squares of nonlinear functions, Department of Computer Science report 71-6, Yale University, New Haven, Connecticut.

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  3. Fletcher, R. [1971]. A modified Marquardt subroutine for nonlinear least squares, Atomic Energy Research Establishment report R6799, Harwell, England.

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  4. Fletcher, R. and Powell, M.J.D. [1963]. A rapidly convergent descent method for minimization, Comput. J. 6, 163–168.

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  5. Hebden, M. D. [1973]. An algorithm for minimization using exact second derivatives, Atomic Energy Research Establishment report TP515, Harwell, England.

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  6. Kowalik, J. and Osborne, M. R. [1968]. Methods for Unconstrained Optimization Problems, American Elsevier.

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  7. Levenberg, K. [1944]. A method for the solution of certain nonlinear problems in least squares, Quart. Appl. Math. 2, 164–168.

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  8. Marquardt, D. W. [1963]. An algorithm for least squares estimation of nonlinear parameters, SIAM J. Appl. Math. 11, 431–441.

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  9. Osborne, M. R. [1972]. Some aspects of nonlinear least squares calculations, in Numerical Methods for Nonlinear Optimization, F. A. Lootsma, ed., Academic Press.

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  10. Osborne, M. R. [1975]. Nonlinear least squares — the Levenberg algorithm revisited, to appear in Series B of the Journal of the Australian Mathematical Society.

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Authors
  1. Jorge J. Moré
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G. A. Watson

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© 1978 Springer-Verlag

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Moré, J.J. (1978). The Levenberg-Marquardt algorithm: Implementation and theory. In: Watson, G.A. (eds) Numerical Analysis. Lecture Notes in Mathematics, vol 630. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0067700

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  • DOI: https://doi.org/10.1007/BFb0067700

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08538-6

  • Online ISBN: 978-3-540-35972-2

  • eBook Packages: Springer Book Archive

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