Solution of lyapunov equations by alternating direction implicit iteration

AbstractIn this report, a new procedure is presented for solving the Lyapunov matrix equation. First, the system is reduced to tridiagonal form with Gaussian similarity transformations. Then the resulting system is solved with Alternating-Direction-Implicit (ADI) iteration. A matrix commutation property essential for “model problem” convergence of ADI iteration applied to elliptic difference equations is not needed for this application. All stable Lyapunov matrix equations are model ADI problems