Geodesic
Generalizations of harmonic and refined Rayleigh-Ritz
Electronic transactions on numerical analysis, Tome 20 (2005), pp. 235-252.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We investigate several generalizations of the harmonic and refined Rayleigh-Ritz method. These may be practical when one is interested in eigenvalues close to one of two targets (for instance, when the eigenproblem has Hamiltonian structure such that eigenvalues come in pairs or quadruples), or in rightmost eigenvalues close to (for instance) the imaginary axis. Our goal is to develop new methods to extract promising approximate eigenpairs from a search space, for instance one generated by the Arnoldi or Jacobi-Davidson method. We give theoretical as well as numerical results of the methods, and recommendations for their use.
Classification : 65F15, 65F50
Keywords: rational harmonic Rayleigh-ritz, rightmost eigenvalue, structured eigenproblem, Hamiltonian matrix, Rayleigh-ritz, harmonic Rayleigh-ritz, refined Rayleigh-ritz, subspace method, subspace extraction, Jacobi- davidson 
@article{ETNA_2005__20__a1,
     author = {Hochstenbach, Michiel E.},
     title = {Generalizations of harmonic and refined {Rayleigh-Ritz}},
     journal = {Electronic transactions on numerical analysis},
     pages = {235--252},
     publisher = {mathdoc},
     volume = {20},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2005__20__a1/}
}
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Hochstenbach, Michiel E. Generalizations of harmonic and refined Rayleigh-Ritz. Electronic transactions on numerical analysis, Tome 20 (2005), pp. 235-252. http://geodesic.mathdoc.fr/item/ETNA_2005__20__a1/