A reduction algorithm for reconstructing periodic Jacobi matrices in Minkowski spaces

The periodic Jacobi inverse eigenvalue problem concerns the reconstruction of a periodic Jacobi matrix from prescribed spectral data. In Minkowski spaces, with a given signature operator H=diag(1,1,…,1,−1), the corresponding matrix is a periodic pseudo-Jacobi matrix. The inverse eigenvalue problem f...

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Bibliographic Details
Published in:Applied mathematics and computation 2022-04, Vol.419, p.126853, Article 126853
Main Authors: Xu, Wei-Ru, Bebiano, Natália, Chen, Guo-Liang
Format: Article
Language:English
Subjects:
Householder transformation
Inverse eigenvalue problem
Lanczos algorithm
Periodic pseudo-Jacobi matrix
Pseudo-Jacobi matrix
Sylvester’s identity
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Summary:The periodic Jacobi inverse eigenvalue problem concerns the reconstruction of a periodic Jacobi matrix from prescribed spectral data. In Minkowski spaces, with a given signature operator H=diag(1,1,…,1,−1), the corresponding matrix is a periodic pseudo-Jacobi matrix. The inverse eigenvalue problem for such matrices consists in the reconstruction of pseudo-Jacobi matrices, with the same order and signature operator H. In this paper we solve this problem by applying Sylvester’s identity and Householder transformation. The solution number and the corresponding reconstruction algorithm are here exhibited, and illustrative numerical examples are given. Comparing this approach with the known Lanczos algorithm for reconstructing pseudo-Jacobi matrices, our method is shown to be more stable and effective.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2021.126853