Perturbation analysis of eigenvalues for second Dirichlet-Neumann tridiagonal Toeplitz matrices

Zhaolin Jiang; Hongxiao Chu; Qiaoyun Miao; Ziwu Jiang; Zhaolin Jiang; Hongxiao Chu; Qiaoyun Miao; Ziwu Jiang

doi:10.3934/math.20251053

AIMS Mathematics

2025, Volume 10, Issue 10: 23697-23714. doi: 10.3934/math.20251053

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Research article

Perturbation analysis of eigenvalues for second Dirichlet-Neumann tridiagonal Toeplitz matrices

1.
School of Intelligent Science and Control Engineering, Shandong Vocational and Technical University of International Studies, Rizhao, 276826, China
2.
School of Mathematics and Statistics, Linyi University, Linyi, 276000, China
3.
School of Mathematics and Statistics, Qingdao University, Qingdao, 266071, China
4.
School of Information Science and Engineering, Linyi University, Linyi, 276000, China

Received: 28 August 2025 Revised: 06 October 2025 Accepted: 10 October 2025 Published: 17 October 2025
MSC : 15B05, 15A12, 15A18

This study focused on tridiagonal Toeplitz matrices based on second Dirichlet-Neumann boundary conditions and conducted in-depth research on their eigenvalue sensitivity. After evaluating condition numbers from both individual and global perspectives using parameters, our framework further achieved spectral sensitivity assessment in the context of second Dirichlet-Neumann tridiagonal Toeplitz matrices. The analysis process examined the $ \varepsilon $-pseudospectra. Finally, we explored an inverse eigenvalue problem embedded in a constrained optimization framework, where the trapezoidal second Dirichlet-Neumann tridiagonal Toeplitz matrix generated by this problem becomes the ultimate optimal computational solution.
- Toeplitz matrix,
- condition number,
- eigenvalue sensitivity,
- inverse eigenvalue problem
Citation: Zhaolin Jiang, Hongxiao Chu, Qiaoyun Miao, Ziwu Jiang. Perturbation analysis of eigenvalues for second Dirichlet-Neumann tridiagonal Toeplitz matrices[J]. AIMS Mathematics, 2025, 10(10): 23697-23714. doi: 10.3934/math.20251053

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Abstract

This study focused on tridiagonal Toeplitz matrices based on second Dirichlet-Neumann boundary conditions and conducted in-depth research on their eigenvalue sensitivity. After evaluating condition numbers from both individual and global perspectives using parameters, our framework further achieved spectral sensitivity assessment in the context of second Dirichlet-Neumann tridiagonal Toeplitz matrices. The analysis process examined the $ \varepsilon $-pseudospectra. Finally, we explored an inverse eigenvalue problem embedded in a constrained optimization framework, where the trapezoidal second Dirichlet-Neumann tridiagonal Toeplitz matrix generated by this problem becomes the ultimate optimal computational solution.

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