Results 141 to 150 of about 753 (179)
Weighted Inner Products for GMRES and GMRES-DR [PDF]
SIAM Journal of Scientific Computing, 2017 Revision containing edits to the text, corrections, and removal of the section on Arnoldi in weighted inner products (to reduce the manuscript's length)
Ronald Benjamin Morgan, Mark Embree
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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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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 Franklin 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 Franklin 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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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 Franklin 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 Benjamin Morgan
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Theoretical and Numerical Comparisons of GMRES and WZ-GMRES
Computers and Mathematics With Applications, 2004 The authors study the numerical stability of the WZ-GMRES method proposed by \textit{H. F. Walker} and \textit{L. Zhou} [Numer. Linear Algebra Appl. 1, No. 6, 571--581 (1994; Zbl 0838.65030)] and compare the stability of the WZ-GMRES method with that of the GMRES method for solving systems of linear equations \(Ax = b\) with a non-symmetric matrix \(A\)
Chen, G. Z., Jia, Z. X.
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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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Some Observations on Weighted GMRES [PDF]
Numerical Algorithms, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Stefan Güttel, Jennifer Pestana
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