Розв’язування систем матричних рівнянь другого степеня: Fìz.-mat. model. ìnf. tehnol. 2021, 33:52-56

• Date: 2021
• Main Author: Nedashkovska, Anastasiya
• Format: Article
• Language: Ukrainian
• Published: Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України 2021
• Subjects: ітераційний метод; системи матричних рівнянь; матричні рівняння другого степеня
• Online Access: https://www.fmmit.lviv.ua/index.php/fmmit/article/view/201
• Journal Title: Physico-mathematical modeling and informational technologies

Matrix equations and systems of matrix equations are widely used in control system optimization problems. However, the methods for their solving are developed only for the most popular matrix equations – Riccati and Lyapunov equations, and there is no universal approach for solving problems of this class. This paper summarizes the previously considered method of solving systems of algebraic equations over a field of real numbers [1] and proposes a scheme for systems of polynomial matrix equations of the second degree with many unknowns. A recurrent formula for fractionalization a solution into a continued matrix fraction is also given. The convergence of the proposed method is investigated. The results of numerical experiments that confirm the validity of theoretical calculations and the effectiveness of the proposed scheme are presented. References Nedashkovska, A. M. (2015). Iteratsiinyi metod rozviazuvannia systemy polinomialnykh rivnian druhoho stepenia. Fizyko-matematychne modeliuvannia ta informatsiini tekhnolohii, 21, 150-161. (in Ukrianian) Lions, Zh.-L. (1972). Optimalnoye upravleniye sistemami. opisyvayemymi uravneniyami s chastnymi proizvodnymi. M.: Mir. Bodnar, D. I. (1986). Vetvyashchiyesya tsepnyye drobi. K.: Naukova dumka. (in Russian).