hrvatski

Problem identifikacije parametara u nekim specijalnim matematičkim modelima

In this thesis we consider the parameter identification problem in some special mathematical models appearing frequently in applied research. First we define the ordinary least squares problem and the total least squares problem, and illustrate this in case of the exponential and the generalized logistic model function. The ordinary least squares is used when the errors occur only in the measured values of the dependent variable, and the total least squares method is used when the errors occur in both the independent and dependent variables. For the given data and for the above model functions we prove the existence theorems for the optimal parameters in the sense of ordinary and in the sense of total least squares. We require only that the data satisfy the natural conditions, such as that the measured values of the dependent variable be positive. We also allow weighted data, which is important for applied research. Also, the methodology is worked out, which can successfully be applied in other similar situations. From the proof of the mentioned theorems, we deduce also a practical method for the choice of a good initial approximation of the optimal parameters. In addition, we propose an efficient method for the choice of a good initial approximation of the optimal parameters in a mathematical model described by an ordinary differential equation of the $n!-!th$ degree which can not be integrated in terms of elementary functions.

identifikacija parametara; matematički model

nije evidentirano