Computing unstructured and structured polynomial pseudospectrum approximations

Eigenvector sensitivity under general and structured perturbations of tridiagonal Toeplitz‐type matrices

“…The sensitivity of the eigenvalues of a structured matrix to general or structured perturbations of the matrix entries has received considerable attention in the literature. Both bounds and graphical tools such as the pseudospectrum or structured pseudospectrum have been developed; see, e.g., [5,6,16,19,25,26]. While the pseudospectrum measures the sensitivity of the eigenvalues, it depends on the sensitivity of the eigenvectors of the matrix to perturbations of the matrix entries.…”