engleski

Solving the parameter identification problem by using TL_p spline

We consider the parameter identification problem in the mathematical model described by one differential equation whose solution cannot be represented by elementary functions. In addition to the quasilinearization method, an important method for solving this problem is smoothing the data method. Thereby smoothing the data is usually carried out by applying either the least squares spline or the moving least squares method or wavelets. The ordinary least squares method assumes that errors occur only in measurement of the dependent variable and that they are normally distributed with expectancy zero. In this paper we also assume that the additive errors can also appear in the measured values of the independent variable, as well as that among the data the so-called outliers can appear. Therefore, for smoothing the data we will use the so-called total L_1 natural cubic spline, i.e. in general, the total L_p (p equals and greater than 1) natural cubic spline. Thereby we will use the method described in the work (1). By the construction of the total L_p natural cubic spline the well known Brent method for onedimensional minimization and Nelder-Meads Downhill Simplex Method or genetic algorithm for function minimization will be used. The mentioned method for solving parameter identification problems will be tested on several numerical examples.

parameter identification ; mathematical model ; smoothing spline

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