The Levenberg-Marquardt algorithm: Implementation and theory

  • Jorge J. Moré
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 630)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bard, Y. [1970]. Comparison of gradient methods for the solution of nonlinear parameter estimation problem, SIAM J. Numer. Anal. 7, 157–186.MathSciNetCrossRefMATHGoogle Scholar
  2. 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.Google Scholar
  3. 3.
    Fletcher, R. [1971]. A modified Marquardt subroutine for nonlinear least squares, Atomic Energy Research Establishment report R6799, Harwell, England.Google Scholar
  4. 4.
    Fletcher, R. and Powell, M.J.D. [1963]. A rapidly convergent descent method for minimization, Comput. J. 6, 163–168.MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Hebden, M. D. [1973]. An algorithm for minimization using exact second derivatives, Atomic Energy Research Establishment report TP515, Harwell, England.Google Scholar
  6. 6.
    Kowalik, J. and Osborne, M. R. [1968]. Methods for Unconstrained Optimization Problems, American Elsevier.Google Scholar
  7. 7.
    Levenberg, K. [1944]. A method for the solution of certain nonlinear problems in least squares, Quart. Appl. Math. 2, 164–168.MathSciNetMATHGoogle Scholar
  8. 8.
    Marquardt, D. W. [1963]. An algorithm for least squares estimation of nonlinear parameters, SIAM J. Appl. Math. 11, 431–441.MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Osborne, M. R. [1972]. Some aspects of nonlinear least squares calculations, in Numerical Methods for Nonlinear Optimization, F. A. Lootsma, ed., Academic Press.Google Scholar
  10. 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.Google Scholar
  11. 11.
    Powell, M. J. D. [1975]. Convergence properties of a class of minimization algorithms, in Nonlinear Programming 2, O. L. Mangasarian, R. R. Meyer, and S. M. Robinson, eds., Academic Press.Google Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • Jorge J. Moré

There are no affiliations available

Personalised recommendations