Shvets O. The adaptive digital data processing approaches by pseudoinversion and structural-parametrical optimization methods

In the thesis adaptive approaches of experimental data approximation on the basis of pseudo-inversion methods and structurally-parametrical optimization are developed. Dynamic models in the ordinary differential systems form and difference equations concerning parameters which define structure of approximating function are constructed. Questions of convergence of continuous and discrete iterative schemes on specification of parameters for approximation of signals in real time are investigated. The theorems of convergence which are proved on Lyapunov's second method and also new results in the field of practical stability are formulated and proved. Thus estimations for the analysis of convergence which connect initial approach, accuracy of approximation on some interval of time and its length are received. New methods of construction of orthogonal transformations which consider structure of experimental data for the decision of some problems of digital processing signals, recognition and classificationsof the voice information are developed for structurally-parametrical representation of approximating function.