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A method for recovering Jacobi matrices with mixed spectral data

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  • Wei, Zhaoying
  • Wei, Guangsheng

Abstract

In this paper we employ the Euclidean division for polynomials to recover uniquely a Jacobi matrix in terms of the mixed spectral data consisting of its partial entries and the information given on its full spectrum together with a subset of eigenvalues of its truncated matrix obtained by deleting the last row and last column, or its rank-one modification matrix modified by adding a constant to the last element. A necessary and sufficient condition is provided for the existence of the inverse problem. A numerical algorithm and a numerical example are given.

Suggested Citation

  • Wei, Zhaoying & Wei, Guangsheng, 2019. "A method for recovering Jacobi matrices with mixed spectral data," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 426-432.
    • Handle: RePEc:eee:apmaco:v:359:y:2019:i:c:p:426-432
    DOI: 10.1016/j.amc.2019.04.050
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    References listed on IDEAS

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    1. Wei, Ying & Dai, Hua, 2015. "An inverse eigenvalue problem for Jacobi matrix," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 633-642.
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