NDLI: Nonlinear Eigenvalue Problems with Specified Eigenvalues

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Kressner, Daniel Mengi, Emre Karow, Michael
Copyright Year	2014
Abstract	This work considers eigenvalue problems that are nonlinear in the eigenvalue parameter. Given such a nonlinear eigenvalue problem $T$, we are concerned with finding the minimal backward error such that $T$ has a set of prescribed eigenvalues with prescribed algebraic multiplicities. We consider backward errors that only allow constant perturbations, which do not depend on the eigenvalue parameter. While the usual resolvent norm addresses this question for a single eigenvalue of multiplicity one, the general setting involving several eigenvalues is significantly more difficult. Under mild assumptions, we derive a singular value optimization characterization for the minimal perturbation that addresses the general case.
Starting Page	819
Ending Page	834
Page Count	16
File Format	PDF
ISSN	08954798
DOI	10.1137/130927462
e-ISSN	10957162
Journal	SIAM Journal on Matrix Analysis and Applications (SJMAEL)
Issue Number	3
Volume Number	35
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2014-07-01
Access Restriction	Subscribed
Subject Keyword	backward error Eigenvalues, eigenvectors analytic matrix-valued function Sylvester-like operator Inverse eigenvalue problems nonlinear eigenvalue problem
Content Type	Text
Resource Type	Article
Subject	Analysis

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