Applications of Mathematics, Vol. 64, No. 3, pp. 351-366, 2019
On the inverse eigenvalue problem for a special kind of acyclic matrices
Mohammad Heydari, Seyed Abolfazl Shahzadeh Fazeli, Seyed Mehdi Karbassi
Received September 6, 2018. Published online April 24, 2019.
Abstract: 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.
Keywords: inverse eigenvalue problem; leading principal minor; graph of a matrix
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