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

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.

@Article{JCM-25-620, author = {}, 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 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 KW - Jacobi matrix KW - Eigenvalue problem KW - 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.