Gauss-Newton gradient technique

The process of parameter identification using the Gauss-Newton gradient technique is especially meant for the cases where we have a complex mathematical model of a process that imposes an attentive numerical processing. 

Here Pij gives the value of the parameter having the number i for the iteration with the number j. The parameter m of the relation (3.238) can be estimated using a variation of the Gauss-Newton gradient technique. The old procedure for the estimation of m starts from the acceptance of the vector of parameters being limited between a minimal and maximal a priori accepted value Pmin N P -< Pmax- Here we can introduce a vector of dimensionless parameters Pnd = (P Pmin)/(Pmax Pmin)> which is ranged between zero and one for the minimal and the maximal values, respectively. With these limit values, we can compute the values of the dimensionless function for P d = 0,0.5, las (0),(D(0. 5) and (1) and then they can be used for the estimation of mp... 

In the relation (3.231) s represents the number of experimental points located on the Zg coordinate while r characterizes the time position when a measure is executed. The base of the development of the Newton-Gauss gradient technique resides in the Taylor expansion Y(z,t, P) near the starting vector of parameters Po ... 

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