Author(s) :
Safique Ahmad
,
Volker Mehrmann
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 01-2014
MSC 2000
- 65F15 Eigenvalues, eigenvectors
-
15A18 Eigenvalues, singular values, and eigenvectors
Abstract :
Minimal structured perturbations are constructed such that an approximate eigenpair
of a nonlinear eigenvalue problem in homogeneous form is an exact eigenpair of
an appropriately perturbed nonlinear matrix function. Structured and unstructured
backward errors are compared. These results extend previous results for (structured) matrix polynomials
to more general functions.
Structured and unstructured pseudospectra for nonlinear
eigenvalue problems are also discussed.
Keywords :
nonlinear eigenvalue problem, backward error, symmetric/skew symmetric eigenvalue problem, Hermiitian/skew-Hermitian eigenvalue problem