Застосування паралельних обчислень при наближеному розв’язуванні однобічних матричних рівнянь
Matrix equations are widely used in optimization problems of control systems. Most often, these are the Ricatti and Sylvester equations, but there are other types of matrix equations. There is no general approach to solving problems of this type, so the development of appro...
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| Datum: | 2023 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Ukrainisch |
| Veröffentlicht: |
Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України
2023
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| Online Zugang: | https://www.fmmit.lviv.ua/index.php/fmmit/article/view/298 |
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| Назва журналу: | Physico-mathematical modeling and informational technologies |
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Physico-mathematical modeling and informational technologies| Zusammenfassung: | Matrix equations are widely used in optimization problems of control systems. Most often, these are the Ricatti and Sylvester equations, but there are other types of matrix equations. There is no general approach to solving problems of this type, so the development of approximate solution schemes is actual. In one of the previous publications, Khovanskyi's method was generalized. An iterative scheme for solving one-sided matrix equations of the form XnAn+Xn-1An-1+…+X2A2+XA1+A0=0. is obtained. The publication presented a recurrent formula for calculating an approximate solution of equations in the form of a continued matrix fraction. Also, the convergence of the proposed method was investigated. In this article, a modification of the previously considered scheme is proposed. Parallel algorithms are applied for matrix multiplication, matrix addition operations and for finding the inverse matrix. |
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