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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.

3 The Gauss-Newton Method The Gauss-Newton method is a method for minimizing a sum-of-squares objective func-tion. It presumes that the objective function is approximately quadratic in the parameters near the optimal solution [2]. For moderately-sized problems the Gauss-Newton method typically converges much faster than gradient-descent methods ...

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