On some numerical methods for solving large-scale differential T-Lyapunov matrix equations

Document Type : Research Paper


Department of Mathematics, Faculty of Science, Chouaib Doukkali University, El Jadida, Morocco


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.


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Volume 13, Issue 2
July 2022
Pages 577-590
  • Receive Date: 19 September 2020
  • Revise Date: 19 November 2020
  • Accept Date: 28 November 2020