Compress‐and‐restart block Krylov subspace methods for Sylvester matrix equations

  title={Compress‐and‐restart block Krylov subspace methods for Sylvester matrix equations},
  author={Daniel Kressner and Kathryn Lund and Stefano Massei and Davide Palitta},
  journal={Numerical Linear Algebra with Applications},
Block Krylov subspace methods (KSMs) comprise building blocks in many state‐of‐the‐art solvers for large‐scale matrix equations as they arise, for example, from the discretization of partial differential equations. While extended and rational block Krylov subspace methods provide a major reduction in iteration counts over polynomial block KSMs, they also require reliable solvers for the coefficient matrices, and these solvers are often iterative methods themselves. It is not hard to devise… 

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An Error Analysis for Rational Galerkin Projection Applied to the Sylvester Equation

  • B. Beckermann
  • Mathematics, Computer Science
    SIAM J. Numer. Anal.
  • 2011
A new formula for the residual of Galerkin projection onto rational Krylov spaces applied to a Sylvester equation is suggested, and a relation to three different underlying extremal problems for rational functions is established.