Krylov Subspace Methods for Large-Scale Constrained Sylvester Equations

We consider the numerical approximation to the solution of the matrix equation A1X+XA2 −Y C = 0 in the unknown matrices X, Y , under the constraint XB = 0, with A1, A2 of large dimensions. We propose a new formulation of the problem that entails the numerical solution of an unconstrained Sylvester equation. The spectral properties of the resulting coefficient matrices call for appropriately designed variants of projection-type methods. To this end, we propose new enriched approximation spaces, and provide experimental evidence of their effectiveness on benchmark problems. The application to a control problem is also described.