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Block Krylov Subspace Methods for Solving Large Sylvester Equations

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Abstract

In the present paper, we propose block Krylov subspace methods for solving the Sylvester matrix equation AX−XB=C. We first consider the case when A is large and B is of small size. We use block Krylov subspace methods such as the block Arnoldi and the block Lanczos algorithms to compute approximations to the solution of the Sylvester matrix equation. When both matrices are large and the right-hand side matrix is of small rank, we will show how to extract low-rank approximations. We give some theoretical results such as perturbation results and bounds of the norm of the error. Numerical experiments will also be given to show the effectiveness of these block methods.

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Authors and Affiliations

  1. Laboratoire d'analyse numérique et d'Optimisation, Bat. M3, Université des sciences et technologies de Lille, F-59655, Villeneuve d'Ascq, France

    A. El Guennouni

  2. Université du Littoral, Zone universitaire de la Mi-voix, Batiment H. Poincaré, 50 rue F. Buisson, BP 699, F-62228, Calais Cedex, France

    K. Jbilou & A.J. Riquet

Authors
  1. A. El Guennouni
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  2. K. Jbilou
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  3. A.J. Riquet
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El Guennouni, A., Jbilou, K. & Riquet, A. Block Krylov Subspace Methods for Solving Large Sylvester Equations. Numerical Algorithms 29, 75–96 (2002). https://doi.org/10.1023/A:1014807923223

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