Sensitivity Analysis of Eigenvalues for PDNT Toeplitz Matrices

This study focuses on a class of perturbed Dirichlet–Neumann tridiagonal (PDNT) Toeplitz matrices, mainly exploring their eigenvalue sensitivity and inverse problems. By the explicit expressions for eigenvalues and eigenvectors of PDNT Toeplitz matrices, an analytical formula for the eigenvalue condition number is proposed, and numerical experiments are presented based on the theoretical results. Meanwhile, the stability of eigenvalues is analyzed with respect to structured perturbations and pseudospectral properties, and finally, two inverse eigenvalue problems are discussed.