Low rank rational perturbations of linear symmetric eigenproblems
Леонід Іванович Мазуренко, H. Voss · ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik · 2006
Abstract 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.