Advances in Computational Mathematics

, Volume 8, Issue 1–2, pp 33–48 | Cite as

Numerical solution of generalized Lyapunov equations

  • Thilo Penzl


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.

mathematical software generalized Lyapunov equation generalized Stein equation condition estimation 65F05 65F15 93B40 93B51 


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Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Thilo Penzl
    • 1
  1. 1.Fakultät für MathematikTechnische Universität Chemnitz–ZwickauChemnitzGermany

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