Numerical solution of generalized Lyapunov equations

Two efficient methods for solving generalized Lyapunov equations and their implementations in FORTRAN 77 are presented. The first 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 flexible way. They can handle the transposed equations and provide scaling to avoid overflow in the solution. Moreover, the Bartels–Stewart subroutine offers 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.

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