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Implementation of a high-order spatial discretization into a finite volume solver: Applications to turbomachinery test cases using an eddy-viscosity turbulence closure. [PDF]
HeliyonRosafio N, Salvadori S, Misul DA.
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Proxy-GMRES: Preconditioning via GMRES in Polynomial Space
SIAM Journal on Matrix Analysis and Applications, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xin Ye, Yuanzhe Xi, Yousef Saad
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Polynomial Preconditioned GMRES and GMRES-DR
SIAM Journal on Scientific Computing, 2015Summary: We look at solving large nonsymmetric systems of linear equations using polynomial preconditioned Krylov methods. We give a simple way to find the polynomial. It is shown that polynomial preconditioning can significantly improve restarted GMRES for difficult problems, and the reasons for this are examined.
Liu, Quan +2 more
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Adaptively Preconditioned GMRES Algorithms
SIAM Journal on Scientific Computing, 1998Summary: The restarted GMRES algorithm proposed by \textit{Y. Saad} and \textit{M. H. Schultz} [SIAM J. Sci. Statist. Comput. 7, 856-869 (1986; Zbl 0599.65018)] is one of the most popular iterative methods for the solution of large linear systems of equations \(Ax=b\) with a nonsymmetric and sparse matrix. This algorithm is particularly attractive when
Baglama, J. +3 more
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Numerical Linear Algebra with Applications, 1994
AbstractThe generalized minimal residual (GMRES) method is widely used for solving very large, nonsymmetric linear systems, particularly those that arise through discretization of continuous mathematical models in science and engineering. By shifting the Arnoldi process to begin with Ar0 instead of r0, we obtain simpler Gram–Schmidt and Householder ...
Walker, Homer F., Zhou, Lu
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AbstractThe generalized minimal residual (GMRES) method is widely used for solving very large, nonsymmetric linear systems, particularly those that arise through discretization of continuous mathematical models in science and engineering. By shifting the Arnoldi process to begin with Ar0 instead of r0, we obtain simpler Gram–Schmidt and Householder ...
Walker, Homer F., Zhou, Lu
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SIAM Journal on Matrix Analysis and Applications, 1997
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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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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GMRES with Deflated Restarting
SIAM Journal on Scientific Computing, 2002A new version of the generalized minimal residuum (GMRES) algorithm for solving large systems of linear equations is described. It uses a ``deflated restarting'' and at each cycle a recurrence similar to the Arnoldi's one is generated. The new algorithm has about the same storage and expense requirements as GMRES with implicitly restarted Arnoldi ...
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Flexible GMRES with Deflated Restarting
SIAM Journal on Scientific Computing, 2010In many situations, it has been observed that significant convergence improvements can be achieved in preconditioned Krylov subspace methods by enriching them with some spectral information. On the other hand, effective preconditioning strategies are often designed where the preconditioner varies from one step to the next so that a flexible Krylov ...
Giraud, Luc +3 more
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