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## Backward errors and pseudospectra for structured nonlinear eigenvalue problems

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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