A convergence analysis of GMRES and FOM methods for Sylvester equations

Robbe, M.;Sadkane, M
(2002) Numerical Algorithms — Vol. 30, n° 1, p. 71-89 (2002)

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  • Robbe, M.
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  • Sadkane, M
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Abstract
We discuss convergence properties of the GMRES and FOM methods for solving large Sylvester equations of the form AX-XB=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.
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Robbe, M., & Sadkane, M. (2002). A convergence analysis of GMRES and FOM methods for Sylvester equations. Numerical Algorithms, 30(1), 71-89. https://doi.org/10.1023/A:1015615310584 (Original work published 2002)