CASPIAN JOURNAL
MANAGEMENT AND HIGH TECHNOLOGIES
Mathematical description of three dimensional essentially nonlinear dependence on experimental data by Cut-Glue approximation method
 |
Read | Neydorf R.A., Poliakh V. V. Mathematical description of three dimensional essentially nonlinear dependence on experimental data by Cut-Glue approximation method // Caspian journal : management and high technologies. — 2018. — №3. — pp. 10-19. |
Neydorf R.A. - Doct. Sci. (Engineering), Professor, Don State Technical University, 1 Gagarin Sq., Rostov-on-Don, 344000, Russian Federation, ranpro@mail.ru
Poliakh V. V. - post-graduate student, Don State Technical University, 1 Gagarin Sq., Rostov-on-Don, 344000, Russian Federation, silvervpolyah@gmail.com
The obligatory stage of solving complex engineering problems is the construction of mathematical models, developed technical systems. At experimental construction of models of such objects, the approximation of dependences of the output data from input is applied. With their essential non-linearity, the approximation problem becomes time-consuming, significant errors are inevitable. The method of "Cut-Glue" approximation is based on analytical multiplicative "cutting" of data fragments, their approximation by analytical functions and additive "gluing" into a single analytic function. The overall accuracy of the object description by this function is determined by the local errors in the approximation of each fragment. Therefore, ensuring the accuracy of the description of each fragment is an important stage of the method. The exponential dependence of the dimension of the problem on the dimension of the object and the number of fragments makes the structural-parametric minimization of the mathematical model of each fragment actual.
Key words: аппроксимация, структурно-параметрическая оптимизация, эволюционно-генетический алгоритм, комбинаторика, cut-glue, approximation, structural-parametric optimization, evolutionary-genetic algorithm, combinatorics, cut-glue