<p>We present an iteration method for solving a class of indefinite complex symmetric system of linear equations. We prove that the method is unconditionally convergent. The induced preconditioner is utilized to accelerate the convergence of the flexible GMRES method for solving the system. In the implementation of the preconditioner, the subsystems can be solved efficiently using a Krylov subspace method in conjunction with the well-known PRESB preconditioner or the conjugate gradient method. Numerical results are presented to demonstrate the effectiveness of the preconditioner.</p>

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A Preconditioner for Complex Symmetric System of Linear Equations with Indefinite Hermitian Part

  • Davod Khojasteh Salkuyeh

摘要

We present an iteration method for solving a class of indefinite complex symmetric system of linear equations. We prove that the method is unconditionally convergent. The induced preconditioner is utilized to accelerate the convergence of the flexible GMRES method for solving the system. In the implementation of the preconditioner, the subsystems can be solved efficiently using a Krylov subspace method in conjunction with the well-known PRESB preconditioner or the conjugate gradient method. Numerical results are presented to demonstrate the effectiveness of the preconditioner.