Krylov Subspace Methods for Large-Scale Constrained Sylvester Equations
Stephen D. Shank, Valeria Simoncini · SIAM Journal on Matrix Analysis and Applications · 2013
We consider the numerical approximation to the solution of the matrix equation $A_1 X + X A_2 - Y C =0$ in the unknown matrices $X$, $Y$, under the constraint $XB=0$, with $A_1, A_2$ 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.