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Name:  
Miloslav Znojil  
Reviewer number:  
9589  
Email:  
znojil@ujf.cas.cz  
Item's zblNumber:  
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:  
 
Primary Classification:  
 
Secondary Classification:  
 
Keywords:  
complex matrix; eigenvalue problem; Newton and GaussNewton 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) nonanalytic (and, in particular, nondifferentiable) 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 GaussNewton) Method the author demonstrates the merits of his/her approach on five standard numerical examples.  
Remarks to the editors:  