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Name:

Miloslav Znojil

Reviewer number:

9689

Email:

znojil@ujf.cas.cz

Item's zbl-Number:

DE015465451

Author(s):

Sameh, Ahmed; Tong, Zhanye:

Shorttitle:

Trace minimization method for symmetric generalized eigenvalue problem.

Source:

J. Comput. Appl. Math. 123, No. 1-2, 155-175 (2000).

Classification:

65F15

Eigenvalues, eigenvectors

Primary Classification:

Secondary Classification:

Keywords:

Eigenvector, eigenvalue, Jacobi-Davidson scheme, version with the minimized trace.

Review:

With solutions of a generalized eigenvalue problem (for the lowest
part of the spectrum) kept in mind, the authors start from a
Rayleigh-Ritz process on a subspace and from its (favorable)
comparison with the method of minimization of trace. Still they
notice, step-by-step, several merits of the latter approach (first
of all, its capability of avoidance of stagnation in larger
dimensions) and remove some of its shortcomings (in particular,
using an elaborate shifting strategy). In order not to weaken the
robustness of such an approach (endangered by the unstable
convergence), they finally propose the use of the expanding
subspaces in the Lanczos and Davidson spirit. This gives their
final proposal which can be understood as an improved
Jacobi-Davidson scheme and compares very well with it standard
block version, especially when the initial subspace is not
optimal.

Remarks to the editors: