Numerical Algorithms

, Volume 30, Issue 1, pp 71–89

A Convergence Analysis of Gmres and Fom Methods for Sylvester Equations

  • Mickaël Robbé
  • Miloud Sadkane


We discuss convergence properties of the GMRES and FOM methods for solving large Sylvester equations of the form AXXB=C. In particular we show the importance of the separation between the fields of values of A and B on the convergence behavior of GMRES. We also discuss the stagnation phenomenon in GMRES and its consequence on FOM. We generalize the issue of breakdown in the block-Arnoldi algorithm and explain its consequence on FOM and GMRES methods. Several numerical tests illustrate the theoretical results.

Sylvester equation GMRES FOM block Krylov subspace stagnation breakdown 


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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Mickaël Robbé
    • 1
  • Miloud Sadkane
    • 2
  1. 1.Free Field TechnologiesLouvain-la-NeuveBelgium
  2. 2.Département de MathématiquesUniversité de Bretagne OccidentaleBrest CedexFrance

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