The BGMRES Method for Generalized Sylvester Matrix Equation AXB − X = C and Preconditioning

In this paper, we present the block generalized
minimal residual (BGMRES) method in order to solve the
generalized Sylvester matrix equation. However, this method may
not be converged in some problems. We construct a polynomial
preconditioner based on BGMRES which shows why polynomial
preconditioner is superior to some block solvers. Finally, numerical
experiments report the effectiveness of this method.

Authors:

• Azita Tajaddini
• Ramleh Shamsi

Keywords:

• Linear matrix equation
• Block GMRES
• matrix Krylov subspace
• polynomial preconditioner.

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