From low-rank approximation to an efficient rational Krylov subspace method for the Lyapunov equation
This work provides a more efficient method for solving Lyapunov equations, which are important in control theory and model reduction.
The authors propose a new rational Krylov subspace method for solving the Lyapunov equation with rank-1 right-hand side, using adaptively computed shifts derived from low-rank approximation. Numerical experiments demonstrate its effectiveness.
We propose a new method for the approximate solution of the Lyapunov equation with rank-$1$ right-hand side, which is based on extended rational Krylov subspace approximation with adaptively computed shifts. The shift selection is obtained from the connection between the Lyapunov equation, solution of systems of linear ODEs and alternating least squares method for low-rank approximation. The numerical experiments confirm the effectiveness of our approach.