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Backward errors and pseudospectra for structured nonlinear eigenvalue problems

Ahmad, Sk. Safique; Mehrmann, Volker

Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin

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.