A reduction algorithm for reconstructing periodic Jacobi matrices in Minkowski spaces

Wei-Ru Xu, Natália Bebiano and Guo-Liang Chen

Applied Mathematics and Computation, 2022, vol. 419, issue C

Abstract: 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.

Keywords: Inverse eigenvalue problem; Pseudo-Jacobi matrix; Periodic pseudo-Jacobi matrix; Sylvester’s identity; Householder transformation; Lanczos algorithm (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:419:y:2022:i:c:s009630032100936x

DOI: 10.1016/j.amc.2021.126853

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