Speaker
Description
We consider the solution of sequences of parametrized Lyapunov equations. Solutions of such equations can be encountered in many application settings, and they are often intermediate steps of an overall procedure whose main goal is the computation of quantities of the form $f(X)$ where $X$ denotes the solution of a Lyapunov equation.
We are interested in addressing problems where the parameter dependency of the coefficient matrix is encoded as a low-rank modification to a seed, fixed matrix. We propose two novel numerical procedures that fully exploit such a standard structure. The first one builds upon recycling Krylov techniques, and it is well-suited for small dimensional problems as it uses dense numerical linear algebra tools. The second algorithm can instead address large-scale problems by relying on state-of-the-art projection techniques based on the extended Krylov subspace.
We test the new algorithms on several problems arising in the study of damped vibrational systems and the analyses of output synchronization problems for multi-agent systems.
