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Low rank rational perturbations of linear symmetric eigenproblems
Author(s) -
Mazurenko L.,
Voss H.
Publication year - 2006
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200510267
Subject(s) - eigenvalues and eigenvectors , rank (graph theory) , mathematics , limit (mathematics) , vibration , mathematical analysis , embedding , eigenvalue perturbation , pure mathematics , combinatorics , physics , computer science , quantum mechanics , artificial intelligence
In this paper we study low rank rational perturbations of linear symmetric eigenvalue problems which for example govern free vibrations of mechanical structures with elastically attached loads, or mechanical vibrations of fluid–solid structures. Embedding the underlying rational eigenproblem into a parameter dependent family of linear eigenproblems, and examining the limit behaviour of the eigenvalues as the parameter approaches a pole, we determine the number of eigenvalues of the rational problem between two consecutive poles.