Acceleration and stabilization techniques for the Levenberg-Marquardt method

Hiroyasu Sakamoto, Katsuya Matsumoto, Azusa Kuwahara, Yoshiteru Hayami

    Research output: Contribution to journalArticlepeer-review

    11 Citations (Scopus)


    In this paper, two techniques are proposed for accelerating and stabilizing the Levenberg-Marquardt (LM) method where its conventional stabilizer matrix (identity matrix) is superseded by (1) a diagonal matrix whose elements are column norms of Jacobian matrix J, or (2) a non-diagonal square root matrix of JTJ. Geometrically, these techniques make constraint conditions of the LM method fitted better to relevant cost function than conventional one. Results of numerical simulations show that proposed techniques are effective when both column norm ratio of J and mutual interactions between arguments of the cost function are large. Especially, the technique (2) introduces a new LM method of damped Gauss-Newton (GN) type which satisfies both properties of global convergence and quadratic convergence by controlling Marquardt factor and can stabilize convergence numerically. Performance of the LMM techniques are compared also with a damped GN method with line search procedure.

    Original languageEnglish
    Pages (from-to)1971-1977
    Number of pages7
    JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
    Issue number7
    Publication statusPublished - Jul 2005

    All Science Journal Classification (ASJC) codes

    • Signal Processing
    • Applied Mathematics
    • Electrical and Electronic Engineering
    • Computer Graphics and Computer-Aided Design


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