Results 181 to 190 of about 3,479 (214)
GMRES On (Nearly) Singular Systems [PDF]
SIAM Journal on Matrix Analysis and Applications, 1997 The authors' purpose is to examine the behavior of the GMRES method when the matrix \(A\) is singular or nearly so, i.e., ill-conditioned, and to formulate practically effective ways of recognizing the singularity or the ill-conditioning when it might significantly affect the performance of the method.
Peter N Brown, Homer F Walker
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GMRES with Deflated Restarting
SIAM Journal of 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 ...
Ronald B Morgan
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The Tortoise and the Hare Restart GMRES [PDF]
SIAM Review, 2003 Summary: When solving large nonsymmetric systems of linear equations with the restarted generalized minimal residual (GMRES) algorithm, one is inclined to select a relatively large restart parameter in the hope of mimicking the full GMRES process.
Mark Embree
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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.
Quan Liu +2 more
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International Journal of Computer Mathematics, 1996
GMRES method [4] is an effective conjugate gradient-like iterative method for solving linear systems of equations. In each loop of the GMRES we have to solve a special least squares problem (1). A classical way of solving such least squares problems is to factor H into QR using Givens plane rotations.
Changjun Li, David J. Evans 0001
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GMRES method [4] is an effective conjugate gradient-like iterative method for solving linear systems of equations. In each loop of the GMRES we have to solve a special least squares problem (1). A classical way of solving such least squares problems is to factor H into QR using Givens plane rotations.
Changjun Li, David J. Evans 0001
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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
James Baglama +3 more
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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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Analysis of an Implicitly Restarted Simpler GMRES Variant of Augmented GMRES
2010We analyze a Simpler GMRES variant of augmented GMRES with implicit restarting for solving nonsymmetric linear systems with small eigenvalues. The use of a shifted Arnoldi process in the Simpler GMRES variant for computing Arnoldi basis vectors has the advantage of not requiring an upper Hessenberg factorization and this often leads to cheaper ...
Ravindra Boojhawon +3 more
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Simpler GMRES with deflated restarting
Mathematics and Computers in Simulation, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yiqin Lin, Liang Bao, Qinghua Wu
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On GMRES-Equivalent Bounded Operators
SIAM Journal on Matrix Analysis and Applications, 2000The author studies the generalized minimal residual (GMRES) method applied to some operator equation \(Ax= r\) in a Hilbert space \(H\), where the operator \(A\in L(H)\) is supposed to be linear and bounded. At the \(k\)th step, the GMRES produces an approximate solution which minimizes the residual norm \(\|Ax-r\|\) over the Krylov subspace \(K^k(A,r):
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