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

Authors: Azita Tajaddini, Ramleh Shamsi


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.

Keywords: Linear matrix equation, Block GMRES, matrix Krylov subspace, polynomial preconditioner.

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