Generalized Epsilon-Pseudospectra

TL;DR

This paper extends the concept of epsilon-pseudospectra and its computational methods to generalized eigenvalue problems, utilizing rank one perturbations for analysis.

Contribution

It introduces a generalized framework for epsilon-pseudospectra applicable to broader eigenvalue problems and develops associated computational algorithms.

Findings

Generalized epsilon-pseudospectra framework established.

Algorithms for computing generalized epsilon-pseudospectra developed.

Enhanced understanding of eigenvalue sensitivity in generalized problems.

Abstract

We generalize $\epsilon$-pseudospectra and the associated computational algorithms to the generalized eigenvalue problem. Rank one perturbations are used to determine the $\epsilon$-pseudospectra.