Acceleration and Stabilization Techniques for the Levenberg-Marquardt Method
Autor: | Katsuya Matsumoto, Hiroyasu Sakamoto, Azusa Kuwahara, Yoshiteru Hayami |
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Rok vydání: | 2005 |
Předmět: |
Line search
Applied Mathematics Identity matrix Computer Graphics and Computer-Aided Design Levenberg–Marquardt algorithm symbols.namesake Rate of convergence Control theory Norm (mathematics) Signal Processing Jacobian matrix and determinant Diagonal matrix symbols Applied mathematics Electrical and Electronic Engineering Square root of a matrix Mathematics |
Zdroj: | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences. :1971-1978 |
ISSN: | 1745-1337 0916-8508 |
DOI: | 10.1093/ietfec/e88-a.7.1971 |
Popis: | 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and stabilizing the Levenberg-Marquardt (LM) method where its conventional stabilizer matrix (identity matrix) is superseded by (1) a diagonal matrix whose elements are column norms of Jacobian matrix J, or (2) a non-diagonal square root matrix of JTJ.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. |
Databáze: | OpenAIRE |
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