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Volume 25, Issue 5
An Inverse Eigenvalue Problem for Jacobi Matrices

Haixia Liang & Erxiong Jiang

J. Comp. Math., 25 (2007), pp. 620-630.

Published online: 2007-10

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  • Abstract

In this paper, we discuss an inverse eigenvalue problem for constructing a $2n\times 2n$ Jacobi matrix $T$ such that its $2n$ eigenvalues are given distinct real values and its leading principal submatrix of order $n$ is a given Jacobi matrix. A new sufficient and necessary condition for the solvability of the above problem is given in this paper. Furthermore, we present a new algorithm and give some numerical results.

  • Keywords

Symmetric tridiagonal matrix, Jacobi matrix, Eigenvalue problem, Inverse eigenvalue problem.

  • AMS Subject Headings

65L09.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-25-620, author = {Haixia Liang and Erxiong Jiang}, title = {An Inverse Eigenvalue Problem for Jacobi Matrices}, journal = {Journal of Computational Mathematics}, year = {2007}, volume = {25}, number = {5}, pages = {620--630}, abstract = {

In this paper, we discuss an inverse eigenvalue problem for constructing a $2n\times 2n$ Jacobi matrix $T$ such that its $2n$ eigenvalues are given distinct real values and its leading principal submatrix of order $n$ is a given Jacobi matrix. A new sufficient and necessary condition for the solvability of the above problem is given in this paper. Furthermore, we present a new algorithm and give some numerical results.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8717.html} }
TY - JOUR T1 - An Inverse Eigenvalue Problem for Jacobi Matrices AU - Haixia Liang & Erxiong Jiang JO - Journal of Computational Mathematics VL - 5 SP - 620 EP - 630 PY - 2007 DA - 2007/10 SN - 25 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8717.html KW - Symmetric tridiagonal matrix, Jacobi matrix, Eigenvalue problem, Inverse eigenvalue problem. AB -

In this paper, we discuss an inverse eigenvalue problem for constructing a $2n\times 2n$ Jacobi matrix $T$ such that its $2n$ eigenvalues are given distinct real values and its leading principal submatrix of order $n$ is a given Jacobi matrix. A new sufficient and necessary condition for the solvability of the above problem is given in this paper. Furthermore, we present a new algorithm and give some numerical results.

Haixia Liang and Erxiong Jiang. (2007). An Inverse Eigenvalue Problem for Jacobi Matrices. Journal of Computational Mathematics. 25 (5). 620-630. doi:
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