Transcription of The Levenberg-Marquardt algorithm for nonlinear least ...
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The Levenberg-Marquardt algorithm for nonlinear least ...
The Levenberg-Marquardt algorithm fornonlinear least squares curve-fitting problems Henri P. GavinDepartment of Civil and Environmental EngineeringDuke UniversitySeptember 18, 2020 AbstractThe Levenberg-Marquardt algorithm was developed in the early 1960 s to solvenonlinear least squares problems. least squares problems arise in the context of fit-ting a parameterized mathematical model to a set of data points by minimizing anobjective expressed as the sum of the squares of the errors between the model functionand a set of data points. If a model is linear in its parameters, the least squares ob-jective is quadratic in the parameters. This objective may be minimized with respectto the parameters in one step via the solution to a linear matrix equation. If the fitfunction is not linear in its parameters, the least squares problem requires an itera-tive solution algorithm .
4 The Levenberg-Marquardt algorithm for nonlinear least squares If in an iteration ρ i(h) > 4 then p+h is sufficiently better than p, p is replaced by p+h, and λis reduced by a factor.Otherwise λis increased by a factor, and the algorithm proceeds to the next iteration. 4.1.1 Initialization and update of the L-M parameter, λ, and the parameters p In lm.m users may select one of three ...
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