Registration Number
0210U003535,
0108U000749
, R & D reports
Title
Mathematical methods of research of the dynamic and adaptive systems and optimization tasks.
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Head
Prytula M., Bartish M.,
Registration Date
09-02-2010
Organization
Ivan Franko National University of Lviv
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The purpose of work: conducting of local and unlocal reductions is on invariant підмноговиди of the nonlinear dynamic systems; construction and research of new more effective, than known, iteratsiynikh methods for untiing of nonlinear functional equalizations and tasks of optimization. The organization of a research was carried out in next directions: Based on the Bogolubov-Prykar- patsky gradient-holonomic algorithm devised for studying the integrability of nonlinear dynamical system on functional manifolds an exact linearization of a nonlinear Burgers-Korteweg-de Vries type dynamical system is stated. As a corollary, the linear structure of the solution space is described, its connection with the convexity of some functional submanifolds is shown. The bi-hamiltonicity of the Burgers-Korteweg-de Vries system is also stated an infinite hierarchy of functionally independent invariants is constructed. Presents an approach for optimisation of the Kohonen's learning algorithm for Self-Organising Maps. The comparative simulations between classical Kohonen's algorithm and "Neural migration" have been performed using three popular data sets: Animal Database, Iris Database and Servo Database. The comparison itself was based on three criteria - mean square error (MSE), topographic error (TE) and PSR. The new approach for building algorithms for solving of unconstrained minimization problem is proposed. New three-step algorithm is based on gradient method and chord method. The rate of convergence of suggested algorithm is established and proved. A numerical investigation of modification and the basis methods is conducted.
Product Description
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Бартіш М.Я.
Гнатишин О.П.
Николайчук Л.В.
Притула М.М.
Шахно С.М.
Щербина Ю.М.
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2020-04-02
