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dc.contributor.advisorPortnoy, Arturo
dc.contributor.authorGozzer-Lozada, Nitzy R.
dc.description.abstractInverse 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.
dc.description.abstractLos problemas inversos son generalmente problemas mal condicionados. Uno de los métodos utilizados para remediar este problema, es la regularización de Tikhonov, que permite obtener buenos resultados siempre y cuando el parámetro regularizador elegido sea el adecuado. Planteamos un método iterativo, denominado método de reexperimentación, que usa regularización sin tener que buscar un parámetro regularizador óptimo usando métodos tradicionales, ya que, en cada iteración, este parámetro se determina con las características inherentes al problema (jacobiano y hessiano de la función a minimizar). Se usan los datos iniciales para obtener una primera aproximación de la solución; luego se ajusta el parámetro de control y se genera un nuevo experimento con nuevos datos. El problema originado se espera que sea mejor condicionado que el anterior. Aplicaremos el método de reexperimentación a un sistema mecánico conformado por dos masas y tres resortes, usando las frecuencias naturales como datos para aproximar parámetros del problema.
dc.subjectInverse problemsen_US
dc.subjectTikhonov regulationsen_US
dc.subjectIterative methoden_US
dc.subject.lcshInverse problems (Differential equations)en_US
dc.subject.lcshParameter estimationen_US
dc.subject.lcshMathematical modelsen_US
dc.subject.lcshIterative method (Mathematics)en_US
dc.titleReexperimentación, un nuevo método para la recuperación de parámetrosen_US
dc.rights.licenseAll rights reserveden_US
dc.rights.holder(c)2010 Nitzy R. Gozzer Lozadaen_US
dc.contributor.committeeRózga, Krzysztof
dc.contributor.committeeRomero, Juan
dc.contributor.representativeCalderón, Andrés Mathematicsen_US
dc.contributor.collegeCollege of Arts and Sciences - Sciencesen_US
dc.contributor.departmentDepartment of Mathematicsen_US

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