Solution of Large Scale Matrix Equations
In this effort we investigate a broad range of matrix equations appearing in basically all other teams. We exploit the strong connection between the solutions of certain Sylvester equations and moment matching model order reduction to apply our speciallized solvers for so called sparse-dense Sylvester equations. For the different balancing based model reduction approaches we compute factored solutions of (differential) Lyapunov and Riccati equations. Moreover we develop structure preserving and -exploiting solvers for a number of Riccati equations appearing in the optimal control of multi-physics PDE control problems.
In collaboration with the scientific computing team we also develop accelerated solvers for matrix equations with dense coefficient matrices.