Construction of an iterative method for solving a class of complex symmetric generalized Lyapunov matrix equation and application to Helmholtz equation | ||
| AUT Journal of Mathematics and Computing | ||
| مقاله 9، دوره 7، شماره 3، پاییز 2026، صفحه 361-376 اصل مقاله (2.08 M) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2025.24112.1366 | ||
| نویسندگان | ||
| Akbar Shirilord؛ Mehdi Dehghan* | ||
| Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology (Tehran polytechnic), No. 424, Hafez Ave., 15914, Tehran, Iran | ||
| چکیده | ||
| The Lyapunov matrix equations occur in many branches of control theory, such as stability analysis and optimal control. In this work, we introduce a novel iterative approach to address the generalized Lyapunov matrix equation within the framework of complex matrices. At each iteration, the procedure involves solving two conventional Lyapunov equations with real-valued coefficient matrices. The scheme incorporates two positive parameters, for which we establish sufficient conditions to guarantee the convergence of the method under certain assumptions. Then we solve the Lyapunov equation arising by applying a finite difference procedure to Helmholtz equation by proposed method. | ||
| کلیدواژهها | ||
| Generalized Lyapunov equation؛ Control theory؛ Helmholtz equation؛ Systems control framework؛ Iterative schemes؛ Convergence condition | ||
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