Eigenvector sensitivity under general and structured perturbations of tridiagonal Toeplitz-type matrices
It addresses the underexplored problem of eigenvector sensitivity for a specific class of structured matrices, offering incremental theoretical insights.
This paper analyzes the sensitivity of eigenvectors of tridiagonal Toeplitz and Toeplitz-type matrices under general and structured perturbations, providing new theoretical bounds.
The sensitivity of eigenvalues of structured matrices under general or structured perturbations of the matrix entries has been thoroughly studied in the literature. Error bounds are available and the pseudospectrum can be computed to gain insight. Few investigations have focused on analyzing the sensitivity of eigenvectors under general or structured perturbations. The present paper discusses this sensitivity for tridiagonal Toeplitz and Toeplitz-type matrices.