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A reduction algorithm for reconstructing periodic Jacobi matrices in Minkowski spaces

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

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.

Suggested Citation

  • Xu, Wei-Ru & Bebiano, Natália & Chen, Guo-Liang, 2022. "A reduction algorithm for reconstructing periodic Jacobi matrices in Minkowski spaces," Applied Mathematics and Computation, Elsevier, vol. 419(C).
    • Handle: RePEc:eee:apmaco:v:419:y:2022:i:c:s009630032100936x
    DOI: 10.1016/j.amc.2021.126853
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    References listed on IDEAS

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    1. Akritas, Alkiviadis G. & Akritas, Evgenia K. & Malaschonok, Genadii I., 1996. "Various proofs of Sylvester's (determinant) identity," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 42(4), pages 585-593.
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    Cited by:

    1. Zhihan Chen & Weilun Huang, 2023. "Evolutionary Game Analysis of Governmental Intervention in the Sustainable Mechanism of China’s Blue Finance," Sustainability, MDPI, vol. 15(9), pages 1-37, April.

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