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This is a Quantitative Study study.

October 1, 2025Open Access

Sensitivity Analysis of Eigenvalues for PDNT Toeplitz Matrices

ZJZhaolin JiangLinyi University HCHui-Hui ChuLinyi University QMQiaoyun MiaoQingdao University

Key Points

Eigenvalue sensitivity is explored for PDNT Toeplitz matrices, revealing important stability insights.
An analytical formula for the eigenvalue condition number shows significant findings from numerical experiments.
The study focuses on structured perturbations and their influence on the eigenvalue stability in matrices.
Inverse eigenvalue problems are discussed, highlighting potential applications in mathematical modeling.

Abstract

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.

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