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The GMRES algorithm for solving non-Hermitian linear systems \(Ax=b\) \((A\in\mathbb{C}^{N\times N}\), \(b\in \mathbb{C}^{N}\) is studied. The ideal GMRES problem is obtained if one consideres minimization of \(|p(A) |\) instead of \(|p(A)b|\) as in the GMRES algorithm.
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