Numerical methods for differential linear matrix equations via Krylov subspace methods
This work provides computational tools for solving differential matrix equations, which are important in control theory and dynamical systems, but the methods are incremental extensions of existing Krylov subspace approaches.
The paper develops numerical methods for large differential linear matrix equations, using Krylov subspace techniques to produce approximate solutions, with numerical experiments demonstrating their effectiveness.
In the present paper, we present some numerical methods for computing approximate solutions to some large differential linear matrix equations. In the first part of this work, we deal with differential generalized Sylvester matrix equations with full rank right-hand sides using a global Galerkin and a norm-minimization approaches. In the second part, we consider large differential Lyapunov matrix equations with low rank right-hand sides and use the extended global Arnoldi process to produce low rank approximate solutions. We give some theoretical results and present some numerical experiments.