Gozzer-Lozada, Nitzy R.

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Reexperimentación, un nuevo método para la recuperación de parámetros
(2010) Gozzer-Lozada, Nitzy R.; Portnoy, Arturo; College of Arts and Sciences - Sciences; Rózga, Krzysztof; Romero, Juan; Department of Mathematics; Calderón, Andrés
Inverse problems are generally ill-conditioned problems. One of the methods used to solve this problem is Tikhonov regularization, giving good results as long as the regularizing parameter chosen is adequate. We propose an iterative method, called the method of re-experimentation, which uses regularization without having to search for an optimal regularizing parameter using traditional methods, since in each iteration, this parameter is determined by the characteristics inherent to the problem (Jacobian and Hessian of the function to be minimized). Initial data are used to obtain a first approximation of the solution, then adjusting the control parameter and generating a new experiment with new data. The new problem generated is expected to be better conditioned than the last. We apply the method of re-experimentation to a mechanical system consisting of two masses and three springs, using the natural frequency data to approximate parameters of the problem.