Geodesic
Homogeneous Jacobi-Davidson
Electronic transactions on numerical analysis, Tome 29 (2008).

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

Summary: We study a homogeneous variant of the Jacobi-Davidson method for the generalized and polynomial eigenvalue problem. While a homogeneous form of these problems was previously considered for the subspace extraction phase, in this paper this form is also exploited for the subspace expansion phase and the projection present in the correction equation. The resulting method can deal with both finite and infinite eigenvalues in a natural and unified way. We show relations with the multihomogeneous Newton method, Rayleigh quotient iteration, and (standard) Jacobi-Davidson for polynomial eigenproblems.
Classification : 65F15, 65F50
Keywords: homogeneous form, quadratic eigenvalue problem, generalized eigenvalue problem, polynomial eigenvalue problem, infinite eigenvalues, correction equation, subspace method, subspace expansion, large sparse matrices, bihomogeneous Newton, multihomogeneous Newton, Rayleigh quotient iteration, Jacobi-davidson 
@article{ETNA_2008__29__a12,
     author = {Hochstenbach, Michiel E. and Notay, Yvan},
     title = {Homogeneous {Jacobi-Davidson}},
     journal = {Electronic transactions on numerical analysis},
     publisher = {mathdoc},
     volume = {29},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2008__29__a12/}
}
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Hochstenbach, Michiel E.; Notay, Yvan. Homogeneous Jacobi-Davidson. Electronic transactions on numerical analysis, Tome 29 (2008). http://geodesic.mathdoc.fr/item/ETNA_2008__29__a12/