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Information × Registration Number 0208U002807, 0105U002232 , R & D reports Title Research of Li-algebraic, iterative methods for the dynamic systems, optimization problems and teaching of neural networks. popup.stage_title Head Prytula Mykola, Registration Date 19-02-2008 Organization Ivan Franko Lviv National University popup.description2 The purpose of the work is consisted in construction and research Li-algebraic methods for solving of nonlinear dynamic system. research new еffective methods for untiing of optimization problems and also development of algoritm of teaching of artifical neuron networks. The organization of a research was carried out in next directions: A new Whitham type nonlinear evolution equation describing short-wave pertubations in a relaxing medium is studied. Making use of the gradient-holonomic analysis, it is stated the bi-Hamiltonicity and integrability of the corresponding dynamical system. Having developed the tanh-function method and maken use of the symbolic computation technique we obtain solution to the inverse modified Korteveg-de Vries dynamical system. Further research of the Self-Organizing Maps has been undertaken with a particular accent on its visualization abilities. The practical aspects of the U-Matrix visualization algorithm are studied, which lead to the developmentof an automated technique for SOM cluster boundaries determination. The evaluation of the proposed technique is based on a set of well known benchmark datasets and a dataset comprised of the real medical data from cardiology. Some iterative-difference methods for solving unconstrained minimization problems, which do not demand evaluation of second derivatives are presented and also the new approach for building algorithms, which are bases on gradient method and Newton method . We have proved theorems where convergence of the proposed methods is justified and rate of convergence is established. Numerical results are presented.5635 Product Description popup.authors popup.nrat_date 2020-04-02 Close