Inverse tridiagonal array eigenvalue inverse problem with double constraints

Yutong Wu; Rao Zhang; Jiaying Tan; Zhibin Li; Lidong Wang

doi:10.1117/12.3025250

21 February 2024 Inverse tridiagonal array eigenvalue inverse problem with double constraints

Yutong Wu, Rao Zhang, Jiaying Tan, Zhibin Li, Lidong Wang

Proceedings Volume 13080, International Conference on Frontiers of Applied Optics and Computer Engineering (AOCE 2024); 130800B (2024) https://doi.org/10.1117/12.3025250
Event: International Conference on Frontiers of Applied Optics and Computer Engineering, 2024, Kunming, China

Abstract

The inverse problem is a problem as opposed to a positive problem, take a classic example, in mystery novels, the murderer’s crime process can only be traced after the occurrence, and the detection process is a typical inverse problem-solving process. With the development of theory, the Jacobi matrix inverse eigenvalue problem has been widely used in many fields. In this paper, we explore the eigenvalue inverse problem of an anti-tridiagonal matrix with double constraints based on the Jacobi matrix, i.e. an anti-tridiagonal matrix is given one of its eigenpairs, and the submatrix formed by crossing out the first row and the last column of the anti-tridiagonal matrix is given one of its eigenpairs. Then the non-zero elements of the matrix are inverted, and the existence and uniqueness of the solution to the given problem are obtained. In the end, we give two numerical examples to verify the correctness and validity of the solution.

(2024) Published by SPIE. Downloading of the abstract is permitted for personal use only.

Citation Download Citation

Yutong Wu, Rao Zhang, Jiaying Tan, Zhibin Li, and Lidong Wang "Inverse tridiagonal array eigenvalue inverse problem with double constraints", Proc. SPIE 13080, International Conference on Frontiers of Applied Optics and Computer Engineering (AOCE 2024), 130800B (21 February 2024); https://doi.org/10.1117/12.3025250

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