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On some numerical methods for solving large-scale differential T-Lyapunov matrix equations | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 51، دوره 13، شماره 2، مهر 2022، صفحه 577-590 اصل مقاله (519.97 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2020.21859.2300 | ||
| نویسندگان | ||
| Lakhlifa Sadek* ؛ Hamad Talibi Alaoui | ||
| Department of Mathematics, Faculty of Science, Chouaib Doukkali University, El Jadida, Morocco | ||
| تاریخ دریافت: 29 شهریور 1399، تاریخ بازنگری: 29 آبان 1399، تاریخ پذیرش: 08 آذر 1399 | ||
| چکیده | ||
| In this paper, we present two new approaches to solve large-scale differential T-Lyapunov equations. The first one is based on the extended block Krylov subspaces, and the second is based on the extended global Krylov subspaces, using the first projection of the initial problem onto an extended block (or global) Krylov subspaces to get a small-scale differential T-Lyapunov equation. The latter problem is resolved by iterative methods (Rosenbrock or BDF method), then the obtained solution is used to create a low-rank approximate solution of the original problem. This process is being replicated, which increases the dimension of the projection space until some planned accuracy is achieved. We give some new theoretical results and numerical experiments then we compare the new approaches. | ||
| کلیدواژه‌ها | ||
| Extended block Krylov؛ Extended global Krylov؛ Low-rank؛ Krylov method؛ Differential T-Lyapunov equation؛ T-Lyapunov equation؛ T-Sylvester equation, Rosenbrock method؛ BDF method | ||
| مراجع | ||
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