Geodesic
On the inverse eigenvalue problem for a special kind of acyclic matrices
Applications of Mathematics, Tome 64 (2019) no. 3, pp. 351-366.

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We study an inverse eigenvalue problem (IEP) of reconstructing a special kind of symmetric acyclic matrices whose graph is a generalized star graph. The problem involves the reconstruction of a matrix by the minimum and maximum eigenvalues of each of its leading principal submatrices. To solve the problem, we use the recurrence relation of characteristic polynomials among leading principal minors. The necessary and sufficient conditions for the solvability of the problem are derived. Finally, a numerical algorithm and some examples are given.
DOI : 10.21136/AM.2019.0242-18
Classification : 05C50, 65F18
Keywords: inverse eigenvalue problem; leading principal minor; graph of a matrix 
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Heydari, Mohammad; Shahzadeh Fazeli, Seyed Abolfazl; Karbassi, Seyed Mehdi. On the inverse eigenvalue problem for a special kind of acyclic matrices. Applications of Mathematics, Tome 64 (2019) no. 3, pp. 351-366. doi : 10.21136/AM.2019.0242-18. http://geodesic.mathdoc.fr/articles/10.21136/AM.2019.0242-18/

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