https://oldena.lpnu.ua/handle/ntb/41498| Title: | Estimation method for a set of solutions to interval system of linear algebraic equationswith optimized «saturated block» selection procedure |
| Other Titles: | Метод оцінюваннямножини розв’язків інтервальної системи лінійних алгебричних рівнянь з оптимізованою процедурою вибору «насиченого блоку» |
| Authors: | Дивак, Микола Олійник, Ірина Dyvak, Mykola Oliynyk, Iryna |
| Affiliation: | Ternopil National Economic University |
| Bibliographic description (Ukraine): | Dyvak M. Estimation method for a set of solutions to interval system of linear algebraic equationswith optimized «saturated block» selection procedure / Mykola Dyvak, Iryna Oliynyk // Computational Problems of Electrical Engineering. — Lviv : Lviv Politechnic Publishing House, 2017. — Vol 7. — No 1. — P. 17–24. |
| Bibliographic description (International): | Dyvak M. Estimation method for a set of solutions to interval system of linear algebraic equationswith optimized «saturated block» selection procedure / Mykola Dyvak, Iryna Oliynyk // Computational Problems of Electrical Engineering. — Lviv : Lviv Politechnic Publishing House, 2017. — Vol 7. — No 1. — P. 17–24. |
| Is part of: | Computational Problems of Electrical Engineering, 1 (7), 2017 |
| Issue: | 1 |
| Volume: | 7 |
| Issue Date: | 19-Feb-2017 |
| Publisher: | Lviv Politechnic Publishing House |
| Place of the edition/event: | Lviv |
| Keywords: | identification interval analysis solutions localization “saturated block” of interval system of linear algebraic equations stochastic method |
| Number of pages: | 8 |
| Page range: | 17-24 |
| Start page: | 17 |
| End page: | 24 |
| Abstract: | Обґрунтовано необхідність застосування нового
методу формування набору базових рівнянь у задачі
локалізації розв’язків інтервальної системи лінійних
алгебричних рівнянь (ІСЛАР) на основі “насиченого
блоку”, який ґрунтується на розв’язуванні оптимізаційної
задачі.
За критерій обрано мінімізацію максимальної похибки
прогнозування інтервальними моделями, параметри яких
належать області локалізації розв’язків ІСЛАР.
Проведено порівняльний аналіз ефективності запро-
понованого методу пошуку оптимального “насиченого
блоку”, порівняно із методами стохастичного пошуку,
зокрема, з лінійною тактикою та за найкращою спробою.
Показано його суттєву перевагу за критерієм мінімуму
обчислювальної складності. The paper substantiates the necessity of applying a new method for the formation of a set of basic equations in the problem of localizing solutions to an interval system of linear algebraic equations (ISLAE) on the basis of a “saturated block”. The method is based on solving the problem of optimization. Th e minimization of the maximal prediction error by using interval models the parameters of which belong to the localization area of ISLAE solutions is chosen as a criterion. A comparative analysis of the effectiveness of the proposed method for finding the optimal “saturated block” and the methods of stochastic search, in particular with linear tactics and by best attempt is conducted. A significant advantage of the proposed method by the criterion of minimum computational complexity is shown |
| URI: | https://ena.lpnu.ua/handle/ntb/41498 |
| ISSN: | 2224-0977 |
| Copyright owner: | © Національний університет „Львівська політехніка“, 2017 © Dyvak M., Oliynyk I., 2017 |
| References (Ukraine): | [1] M. Dyvak, Tasks of mathematical modeling the static systems with interval data. Ternopil, Ukraine, 2011. (Ukrainian) [2] G. Alefeld and J. Herzberger, Introduction to interval computations, Computer Science and Applied Mathematics. New York, USA: Academic Press, Inc. Harcourt Brace Jovanovich Publishers, 1983. [3] S.P. Shary, Algebraic Approach to the Interval Linear Static Identification, Tolerance, and Control Problems, or One More Application of Kaucher Arithmetic, Reliable Computing, vol. 2, no. 1, pp. 3–33, 1996. [4] M. Dyvak, V. Manzhula and O. Kozak, “New method tolerance estimation of the parameters set of interval model based on saturated block of ISLAE”, in Proc. IX–th International Conference CADSM’2007, pp. 376-379, Lviv–Polyana, Ukraine, 2007. [5] L. Rastrigin, Adaptation of complex system. Riga, Latvia: Zinatne, 1981. (Russian) [6] L. Rastrigin, A random search. Moscow, Russia: Znanie, 1979. (Russian) [7] L. Rastrigin, Theory and application of random search, Institute of electronics and computers equipment, Riga, Latvia, 1969. (Russian) [8] L. Rastrigin, Modern principles of management of complex objects. Moscow, Russia: Owls. radio, 1980. (Russian) [9] E. Walter and L. Pronzato, Identification of parametric model from experimental data, London, Berlin, Heidelberg, New York, Paris, Tokyo: Springer, 1997, 413 p. [10] C. F. J. Wu and M. S. Hamada, Experiments: Planning, Analysis and Optimization, Wiley, 2009. [11] M. Dyvak, I. Oliynyk, and P. Stakhiv, “Method of reduction for interval system of linear algebraic equations and its application to modeling of the electric power generated by a small hydroelectric power station”, in Proc. 17th International Conference on Computational Problems of Electrical Engineering, CPEE’ 2016, Sandomierz, Poland, 2016. [12] M. Dyvak and I. Oliynyk, “Method of formation of an optimal “saturated block” in the task of localization of solutions to interval system of linear algebraic equations”, Inductive Modeling of Complex System, no. 8, pp. 79–99, 2016. (Ukrainian) [13] M. Dyvak, I. Oliynyk, V. Manzhula, and R. Shevchuk, “Stochastic method of forming an optimal “saturated block” in the localization task of solutions to interval system of linear algebraic equations”, in Proc. 14th International Conference CADSM (The Experience of Designing and Application of CAD Systems in Microelectronics), pp. 367–371, Lviv, Ukraine, 2017. |
| References (International): | [1] M. Dyvak, Tasks of mathematical modeling the static systems with interval data. Ternopil, Ukraine, 2011. (Ukrainian) [2] G. Alefeld and J. Herzberger, Introduction to interval computations, Computer Science and Applied Mathematics. New York, USA: Academic Press, Inc. Harcourt Brace Jovanovich Publishers, 1983. [3] S.P. Shary, Algebraic Approach to the Interval Linear Static Identification, Tolerance, and Control Problems, or One More Application of Kaucher Arithmetic, Reliable Computing, vol. 2, no. 1, pp. 3–33, 1996. [4] M. Dyvak, V. Manzhula and O. Kozak, "New method tolerance estimation of the parameters set of interval model based on saturated block of ISLAE", in Proc. IX–th International Conference CADSM’2007, pp. 376-379, Lviv–Polyana, Ukraine, 2007. [5] L. Rastrigin, Adaptation of complex system. Riga, Latvia: Zinatne, 1981. (Russian) [6] L. Rastrigin, A random search. Moscow, Russia: Znanie, 1979. (Russian) [7] L. Rastrigin, Theory and application of random search, Institute of electronics and computers equipment, Riga, Latvia, 1969. (Russian) [8] L. Rastrigin, Modern principles of management of complex objects. Moscow, Russia: Owls. radio, 1980. (Russian) [9] E. Walter and L. Pronzato, Identification of parametric model from experimental data, London, Berlin, Heidelberg, New York, Paris, Tokyo: Springer, 1997, 413 p. [10] C. F. J. Wu and M. S. Hamada, Experiments: Planning, Analysis and Optimization, Wiley, 2009. [11] M. Dyvak, I. Oliynyk, and P. Stakhiv, "Method of reduction for interval system of linear algebraic equations and its application to modeling of the electric power generated by a small hydroelectric power station", in Proc. 17th International Conference on Computational Problems of Electrical Engineering, CPEE’ 2016, Sandomierz, Poland, 2016. [12] M. Dyvak and I. Oliynyk, "Method of formation of an optimal "saturated block" in the task of localization of solutions to interval system of linear algebraic equations", Inductive Modeling of Complex System, no. 8, pp. 79–99, 2016. (Ukrainian) [13] M. Dyvak, I. Oliynyk, V. Manzhula, and R. Shevchuk, "Stochastic method of forming an optimal "saturated block" in the localization task of solutions to interval system of linear algebraic equations", in Proc. 14th International Conference CADSM (The Experience of Designing and Application of CAD Systems in Microelectronics), pp. 367–371, Lviv, Ukraine, 2017. |
| Content type: | Article |
| Appears in Collections: | Computational Problems Of Electrical Engineering. – 2017 – Vol. 7, No. 1 |
| File | Description | Size | Format | |
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| 2017v7n1_Dyvak_M-Estimation_method_for_a_set_17-24.pdf | 406.56 kB | Adobe PDF | View/Open | |
| 2017v7n1_Dyvak_M-Estimation_method_for_a_set_17-24__COVER.png | 482.13 kB | image/png | View/Open |
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