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Acceleration and Stabilization Techniques for the Levenberg-Marquardt Method Hiroyasu SAKAMOTO Katsuya MATSUMOTO Azusa KUWAHARA Yoshiteru HAYAMI Publication IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences Vol.E88-A No.7 pp.1971-1978 Publication Date: 2005/07/01 Online ISSN: DOI: 10.1093/ietfec/e88-a.7.1971 Print ISSN: 0916-8508 Type of Manuscript: PAPER Category: Numerical Analysis and Optimization Keyword: Levenberg-Marquardt method, acceleration, stabilization, diagonal and non-diagonal constraint matrices, Full Text: PDF(985.9KB)>>
Summary: 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and stabilizing the Levenberg-Marquardt (LM) method where its conventional stabilizer matrix (identity matrix) is superseded by (1) a diagonal matrix whose elements are column norms of Jacobian matrix J, or (2) a non-diagonal square root matrix of J TJ. 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. | ||||||||||
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