Geodesic
Restarting techniques for the (Jacobi-)Davidson symmetric eigenvalue method
Electronic transactions on numerical analysis, Tome 7 (1998), pp. 163-181
The (Jacobi-)Davidson method, which is a popular preconditioned extension to the Arnoldi method for solving large eigenvalue problems, is often used with restarting. This has significant performance shortcomings, since important components of the invariant subspace may be discarded. One way of saving more information at restart is through "thick" restarting, a technique that involves keeping more Ritz vectors than needed. This technique and especially its dynamic version have proved very efficient for symmetric cases. A different restarting strategy for the Davidson method has been proposed in [14], motivated by the similarity between the spaces built by the Davidson and Conjugate Gradient methods. For the latter method, a three term recurrence implicitly maintains all required information.
Classification : 65F15
Keywords: davidson, Jacobi-davidson, Lanczos, conjugate gradient methods, eigenvalue, implicit restarting, deflation, preconditioning 
@article{ETNA_1998__7__a3,
     author = {Stathopoulos,  Andreas and Saad,  Yousef},
     title = {Restarting techniques for the {(Jacobi-)Davidson} symmetric eigenvalue method},
     journal = {Electronic transactions on numerical analysis},
     pages = {163--181},
     year = {1998},
     volume = {7},
     zbl = {0912.65027},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_1998__7__a3/}
}
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%A Saad,  Yousef
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%J Electronic transactions on numerical analysis
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%F ETNA_1998__7__a3
Stathopoulos,  Andreas; Saad,  Yousef. Restarting techniques for the (Jacobi-)Davidson symmetric eigenvalue method. Electronic transactions on numerical analysis, Tome 7 (1998), pp. 163-181. http://geodesic.mathdoc.fr/item/ETNA_1998__7__a3/