Numerical solution of generalized Lyapunov equations

Two e cient methods for solving generalized Lyapunov equations and their implementations in FORTRAN 77 are presented. The rst one is a generalization of the Bartels{Stewart method and the second is an extension of Hammarling's method to generalized Lyapunov equations. Our LAPACK based subroutines are implemented in a quite exible way. They can handle the transposed equations and provide scaling to avoid over ow in the solution. Moreover, the Bartels{Stewart subroutine o ers the optional estimation of the separation and the reciprocal condition number. A brief description of both algorithms is given. The performance of the software is demonstrated by numerical experiments. Key Words: Mathematical software, generalized Lyapunov equation, generalized Stein equation, condition estimation. AMS(MOS) subject classi cations: 65F05, 65F15, 93B40, 93B51 1 Basic Properties of Generalized Lyapunov Equations Lyapunov equations play an essential role in control theory. In the past few years it...

• Type: Journal
• Year: 1998
• Where: ADCM
• Authors: Thilo Penzl
• Keywords: ADCM 1998, Lyapunov Equation, Stein Equation, Time Lyapunov Equation