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AN EXPLICIT FORMULA FOR THE SPLITTING OF MULTIPLE EIGENVALUES FOR NONLINEAR EIGENVALUE PROBLEMS AND CONNECTIONS WITH THE LINEARIZATION FOR THE DELAY EIGENVALUE PROBLEM.
- Source :
- SIAM Journal on Matrix Analysis & Applications; 2017, Vol. 38 Issue 2, p599-620, 22p
- Publication Year :
- 2017
-
Abstract
- We contribute to the perturbation theory of nonlinear eigenvalue problems in three ways. First, we extend the formula for the sensitivity of a simple eigenvalue with respect to a variation of a parameter to the case of multiple nonsemisimple eigenvalues, thereby providing an explicit expression for the leading coefficients of the Puiseux series of the emanating branches of eigenvalues. Second, for a broad class of delay eigenvalue problems, the connection between the finite-dimensional nonlinear eigenvalue problem and an associated infinite-dimensional linear eigenvalue problem is emphasized in the developed perturbation theory. Finally, in contrast to existing work on analyzing multiple eigenvalues of delay systems, we develop all theory in a matrix framework, i.e., without reduction of a problem to the analysis of a scalar characteristic quasi-polynomial. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 08954798
- Volume :
- 38
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- SIAM Journal on Matrix Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 123852873
- Full Text :
- https://doi.org/10.1137/16M107774X