The generalized conjugate direction method for solving quadratic inverse eigenvalue problems over generalized skew Hamiltonian matrices with a submatrix constraint

Jia Tang; Yajun Xie; Jia Tang; Yajun Xie

doi:10.3934/math.2020237

AIMS Mathematics

2020, Volume 5, Issue 4: 3664-3681. doi: 10.3934/math.2020237

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Research article

The generalized conjugate direction method for solving quadratic inverse eigenvalue problems over generalized skew Hamiltonian matrices with a submatrix constraint

Jia Tang ¹,
Yajun Xie ^{2
,
,}

1.
School of Mathematics and Informatics & FJKLMAA, Fujian Normal University, Fuzhou 350117, P. R. China
2.
School of Technology, Fuzhou University of International Studies and Trade, Fuzhou 350202, P. R. China

Received: 09 January 2020 Accepted: 07 April 2020 Published: 20 April 2020
MSC : 15A57, 15A24

In this paper, we consider a class of constrained quadratic inverse eigenvalue Problem 1.1. Then, a generalized conjugate direction method is proposed to obtain the generalized skew Hamiltonian matrix solutions with a submatrix constraint. In addition, by choosing a special kind of initial matrices, it is shown that the unique least Frobenius norm solutions can be obtained consequently. Some numerical results are reported to demonstrate the efficiency of our algorithm.
Citation: Jia Tang, Yajun Xie. The generalized conjugate direction method for solving quadratic inverse eigenvalue problems over generalized skew Hamiltonian matrices with a submatrix constraint[J]. AIMS Mathematics, 2020, 5(4): 3664-3681. doi: 10.3934/math.2020237

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Abstract

In this paper, we consider a class of constrained quadratic inverse eigenvalue Problem 1.1. Then, a generalized conjugate direction method is proposed to obtain the generalized skew Hamiltonian matrix solutions with a submatrix constraint. In addition, by choosing a special kind of initial matrices, it is shown that the unique least Frobenius norm solutions can be obtained consequently. Some numerical results are reported to demonstrate the efficiency of our algorithm.

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