Definitions for pseudospectra and stability radii of an analytic matrix function are given, where the structure of the function is exploited. Various perturbation measures are considered and computationally tractable formulae are derived. The results are applied to a class of retarded delay differential equations. Special properties of the pseudospectra of such equations are determined and illu...

We analyze a correlated system in equilibrium with special emphasis on non-Hermitian topology inducing skin effect. The pseudospectrum, computed by the real-space dynamical mean field theory, elucidates that additional pseudoeigenstates emerge for open boundary condition contrast to dependence of density states condition. further discuss how line-gap topology, another type affects pseudospectru...

The study of pseudospectra of linear transformations has become a significant part of numerical linear algebra and related areas. A large body of research activity has focused on how to compute these sets for a given spectral problem with, possibly, certain underlying structure. The theme of this paper was motivated by the question: How effective are path-following procedures for tracing the ps...

We correct an error that incurred in our paper published in SIAM J. Numer. Anal. 49 (2011), pp. 1194–1209, and give new algorithms for tracking the boundary of the pseudospectrum which are suitable for large, sparse matrices.