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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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The modified Levenberg-Marquardt method for nonlinear equations with cubic convergence
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by Jinyan Fan PDF
Math. Comp. 81 (2012), 447-466 Request permission

Abstract:

We propose a modified Levenberg-Marquardt method for nonlinear equations, in which not only a LM step but also an approximate LM step are computed at every iteration. To ensure the global convergence of the new method, a new kind of predicted reduction is introduced for the merit function when using the trust region technique. The cubic convergence of the modified LM method is proved under the local error bound condition which is weaker than nonsingularity. Numerical results show that the new method is very efficient and could save many calculations of the Jacobian.
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Additional Information
  • Jinyan Fan
  • Affiliation: Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China
  • Email: jyfan@sjtu.edu.cn
  • Received by editor(s): April 19, 2010
  • Received by editor(s) in revised form: September 20, 2010
  • Published electronically: June 23, 2011
  • Additional Notes: The author was supported by Chinese NSF grants 10871127, 10701056 and the Chenxing Program of SJTU
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 81 (2012), 447-466
  • MSC (2010): Primary 65K05, 90C30
  • DOI: https://doi.org/10.1090/S0025-5718-2011-02496-8
  • MathSciNet review: 2833503