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Name:
Miloslav Znojil
Reviewer number:
9589
Email:
znojil@ujf.cas.cz
Item's zbl-Number:
DE 016 949 057
Author(s):
Ishihara, K.:
Shorttitle:
Iterative methods for eigenvalue problems with normalization condition for a general complex matrix
Source:
Computing [Suppl] 16, 105 - 118 (2001) (volume Topics in Numerical Analysis dedicated to T. Yamamoto). Wien: Springer, G. Alefeld et al (ed).
Classification:
65E05Numerical methods in complex analysis potential theory, etc.
Primary Classification:
65F15Eigenvalues, eigenvectors
Secondary Classification:
65F10Iterative methods for linear systems
Keywords:
complex matrix; eigenvalue problem; Newton and Gauss-Newton interations; nonlinearity causing normalization to one; damped versions of the method; line search algorithm; convergence;
Review:
Once you normalize a complex eigenvector z to one, your
normalization condition is (of course) non-analytic (and, in
particular, non-differentiable) function of the n components of z
so that the Newton's iteration method must be used with due care.
The details are given: After the formulation and proofs of
convergence of the proposed Generalized Damped Newton (and
Gauss-Newton) Method the author demonstrates the merits of his/her
approach on five standard numerical examples.
Remarks to the editors:

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