Results 141 to 150 of about 4,826 (176)
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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.
Kim-Chuan Toh
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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.
Kim-Chuan Toh
exaly +2 more sources
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 Morgan
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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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Multipreconditioned Gmres for Shifted Systems [PDF]
SIAM Journal of Scientific Computing, 2017 An implementation of GMRES with multiple preconditioners (MPGMRES) is proposed for solving shifted linear systems with shift-and-invert preconditioners. With this type of preconditioner, the Krylov subspace can be built without requiring the matrix-vector product with the shifted matrix.
Daniel Szyld +2 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 ...
Homer F Walker
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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 ...
Homer F Walker
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Polynomial Preconditioned GMRES and GMRES-DR
SIAM Journal of 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.
Ronald Morgan, Walter Wilcox
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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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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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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
openaire +1 more source
Some properties of range restricted GMRES methods
Journal of Computational and Applied Mathematics, 2015 International audienceThe GMRES method is one of the most popular iterative schemes for the solution of large linear systems of equations with a square nonsingular matrix.
Lothar Reichel
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