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Abstract: This paper presents a new preconditioning technique for the restarted GMRES algorithm. It is based on an invariant subspace approximation which is updated at each cycle. Numerical examples show that this deflation technique gives a more robust scheme than the restarted algorithm, at a low cost of operations and memory. Keywords: GMRES, preconditioning, invariant subspace, deflation. Subject Classification: 65F10, 65F15 1 (Update)
Context of citations to this paper: More
...in this present paper has the same effect. We note that a similar approach to the deflation approach described here has been developed in [3] in which a preconditioner is built by deflation for restarted GMRES based on approximating and updating an invariant subspace at each...
...a restart. There are essentially two ways that this can be done: an augmented subspace approach [11,5] and a preconditioning approach [7,1]. The first solution retains vectors from the previous restart and adds them to the new subspace. In particular, it investigates saving k...
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A Class of Spectral Two-Level Preconditioners - Carpentieri, Duff, Giraud (2002) (Correct)
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0.5: On the performance of various adaptive preconditioned GMRES.. - Burrage, Erhel (1997) (Correct)
0.4: A Deflation Technique for Linear Systems of Equations - Burrage, Erhel, Pohl, Williams (1994) (Correct)
0.3: The implementation of a Generalized Cross Validation.. - Burrage, Williams.. (1994) (Correct)
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0.4: Deflation for Implicitly Restarted Arnoldi Methods - Sorensen (1998) (Correct)
0.3: Deflation Techniques For An Implicitly Re-Started Arnoldi.. - Lehoucq, Sorensen (1996) (Correct)
0.2: Dynamic Thick Restarting of the Davidson, and the.. - Stathopoulos, Saad, Wu (1996) (Correct)
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9: A restarted GMRES method augmented with eigenvectors (context) - Morgan - 1995
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BibTeX entry: (Update)
J. Erhel, K. Burrage, and B. Pohl. Restarted gmres preconditioned by deflation. Journal of computational and applied mathematics, 1995. To appear. http://citeseer.ist.psu.edu/erhel95restarted.html More
@misc{ erhel95restarted,
author = "J. Erhel and K. Burrage and B. Pohl",
title = "Restarted gmres preconditioned by deflation",
text = "J. Erhel, K. Burrage, and B. Pohl. Restarted gmres preconditioned by deflation.
Journal of computational and applied mathematics, 1995. To appear.",
year = "1995",
url = "citeseer.ist.psu.edu/erhel95restarted.html" }
Citations (may not include all citations):715 Gmres: a generalized minimal residual algorithm for solving .. (context) - Saad, Schultz - 1986
135 A flexible inner-outer preconditioned gmres algorithm - Saad - 1993
51 Practical use of polynomial preconditioning for the conjugat.. (context) - Saad - 1985
49 Templates for the solution of linear systems: building block.. (context) - Barret, Berry et al. - 1993
20 GMRESR : a family of nested GMRES methods (context) - van der Vorst, Vuik - 1992
18 Polynomial preconditioning for conjugate gradient methods (context) - Ashby - 1987
18 The superlinear convergence behaviour of gmres (context) - Van der Vorst - 1993
18 A robust gmres-based adaptive polynomial preconditioning alg.. (context) - Joubert - 1994
13 Stabilization of unstable procedures: the recursive projecti.. (context) - Shroff, Keller - 1993
8 Some observations on the convergence behavior of GMRES (context) - Huang, van der Vorst - 1989
6 An adaptive chebyshev iterative method for nonsymmetric line.. - Reichel, Calvetti et al. - 1994
3 Numerical treatment of bifurcation problems by adaptive cond.. (context) - Jarausch, Mackens - 1987
2 A hybrid gmres algorithm for nonsymmetric linear systems (context) - Noel, Nachtigal et al. - 1992
1 the convergence behaviour of the restarted gmres algorithm f.. (context) - Joubert
1 A deflation technique for linear systems of equations - Kevin, Jocelyne - 1994
1 Adaptive polynomial preconditioning for hermitian indefinite.. (context) - Steven, Ashby et al. - 1989
1 Polynomial preconditioners for conjugate gradient calculatio.. (context) - Olin, Johnson et al. - 1983
1 How fast are nonsymmetric matrix computations (context) - Noel, Nachtigal et al. - 1992
1 A polynomial preconditioner for the gmres algorithm (context) - van Gijzen - 1995
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