Numerical Algorithms

, Volume 32, Issue 1, pp 27–55 | Cite as

A Modified Low-Rank Smith Method for Large-Scale Lyapunov Equations

  • S. Gugercin
  • D.C. Sorensen
  • A.C. Antoulas


In this note we present a modified cyclic low-rank Smith method to compute low-rank approximations to solutions of Lyapunov equations arising from large-scale dynamical systems. Unlike the original cyclic low-rank Smith method introduced by Penzl in [20], the number of columns required by the modified method in the approximate solution does not necessarily increase at each step and is usually much lower than in the original cyclic low-rank Smith method. The modified method never requires more columns than the original one. Upper bounds are established for the errors of the low-rank approximate solutions and also for the errors in the resulting approximate Hankel singular values. Numerical results are given to verify the efficiency and accuracy of the new algorithm.

Lyapunov equation Smith method ADI iteration model reduction 


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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • S. Gugercin
    • 1
  • D.C. Sorensen
    • 2
  • A.C. Antoulas
    • 1
  1. 1.Department of Electrical and Computer Engineering, MS 380Rice UniversityHouston, TXUSA
  2. 2.Department of Computational and Applied Mathematics, MS 134Rice UniversityHouston, TXUSA

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