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Main Title: Nonlinear eigenvalue problems with specified eigenvalues
Author(s): Karow, Michael
Kressner, Daniel
Mengi, Emre
Type: Article
Language Code: en
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 ignificantly more difficult. Under mild assumptions, we derive a singular value optimization characterization for the minimal perturbation that addresses the general case.
Issue Date: 2014
Date Available: 14-Dec-2017
DDC Class: 518 Numerische Analysis
Subject(s): nonlinear eigenvalue problem
analytic matrix-valued function
Sylvester-like operator
backward error
Journal Title: SIAM Journal on Matrix Analysis and Applications
Publisher: Society for Industrial and Applied Mathematics
Publisher Place: Philadelphia, Pa.
Volume: 35
Issue: 3
Publisher DOI: 10.1137/130927462
Page Start: 819
Page End: 834
EISSN: 1095-7162
ISSN: 0895-4798
Appears in Collections:FG Numerische Lineare Algebra » Publications

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