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Computation of multiple eigenvalues and generalized eigenvectors for matrices dependent on parameters
Author(s) -
Mailybaev Alexei A.
Publication year - 2006
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.471
Subject(s) - eigenvalues and eigenvectors , mathematics , algebra over a field , matrix (chemical analysis) , linear algebra , computation , jordan matrix , combinatorics , pure mathematics , physics , algorithm , quantum mechanics , geometry , materials science , composite material
The paper develops Newton's method of finding multiple eigenvalues with one Jordan block and corresponding generalized eigenvectors for matrices dependent on parameters. It computes the nearest value of a parameter vector with a matrix having a multiple eigenvalue of given multiplicity. The method also works in the whole matrix space (in the absence of parameters). The approach is based on the versal deformation theory for matrices. Numerical examples are given. Copyright © 2005 John Wiley & Sons, Ltd.