Registration Number
0224U002001,
0121U110282
, R & D reports
Title
Iterative methods for solving nonlinear operator equations and minimization tasks. Stochastic optimization. Control task with random switching
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Head
Shakhno Stepan M., Доктор фізико-математичних наук
Registration Date
04-02-2024
Organization
Ivan Franko National University of Lviv
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Two-step Kurchatov-type iterative methods for solving nonlinear operator equations using Fréchet derivative approximation of the operator of the nonlinear equation by divided differences were investigated. The local and semi-local convergence of the methods is studied under the conditions that the divided differences of the first order satisfy the generalized Lipshitz conditions. The results of numerical experiments are also given, which confirm the obtained theoretical estimates.
A new variant of the construction of three-step methods for minimizing the function of many variables is considered. The general scheme of construction of such methods, as well as two specific algorithms, are considered. It is proved that the speed of convergence of the proposed algorithms is higher than or equal to the speed of convergence of the basic algorithms.
For the system of stochastic differential equations with Markov switching and impulse disturbance in the Poisson approximation scheme and under the conditions of the existence of a single equilibrium point of the quality criterion, the limit generators of the impulse process and the dynamic system are constructed. In particular, the issue of how the behavior of the limit process depends on the pre-limit normalization of the stochastic system in the ergodic Markov environment is studied.
Product Description
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Bartish Mykhailo Y.
Holub Bogdan M.
Demydyuk MyroslavV/ V.
Kovalchuk Olga V.
Melnychyn Andriy V.
Nedashkovskyy Mykola О.
Nykolaichuk Lesya V.
Ohorodnyk Natalia P.
Chabanyuk Yaroslav M.
Shakhno Stepan M.
Shunkin Yurii V.
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2024-02-04
