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An effective numerical method is presented for optimizing model parameters that can be applied to any type of system of non-linear equations and any number of data-points, which does not require explicit formulation of the objective function or its partial derivatives. The numerics are reduced to solving a non-linear least squares problem, which uses the Levenberg-Marquardt algorithm and the Jacobian is approximated by applying rank-one updates using Broyden's method. An advantage of thisarXiv:2203.04138v1 fatcat:hyjyryvwlzdlfaxta7trs4chbe