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December, 2019 On Inverse Eigenvalue Problems of Quadratic Palindromic Systems with Partially Prescribed Eigenstructure
Kang Zhao, Lizhi Cheng, Anping Liao, Shengguo Li
Taiwanese J. Math. 23(6): 1511-1534 (December, 2019). DOI: 10.11650/tjm/190203

Abstract

The palindromic inverse eigenvalue problem (PIEP) of constructing matrices $A$ and $Q$ of size $n \times n$ for the quadratic palindromic polynomial $P(\lambda) = \lambda^2 A^{\star} + \lambda Q + A$ so that $P(\lambda)$ has $p$ prescribed eigenpairs is considered. This paper provides two different methods to solve PIEP, and it is shown via construction that PIEP is always solvable for any $p$ ($1 \leq p \leq (3n+1)/2$) prescribed eigenpairs. The eigenstructure of the resulting $P(\lambda)$ is completely analyzed.

Citation

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Kang Zhao. Lizhi Cheng. Anping Liao. Shengguo Li. "On Inverse Eigenvalue Problems of Quadratic Palindromic Systems with Partially Prescribed Eigenstructure." Taiwanese J. Math. 23 (6) 1511 - 1534, December, 2019. https://doi.org/10.11650/tjm/190203

Information

Received: 8 March 2018; Revised: 30 June 2018; Accepted: 21 January 2019; Published: December, 2019
First available in Project Euclid: 4 March 2019

zbMATH: 07142984
MathSciNet: MR4033556
Digital Object Identifier: 10.11650/tjm/190203

Subjects:
Primary: ‎15A24‎ , 15A29 , 65F15 , 65F18

Keywords: inverse eigenvalue problem , partially prescribed eigendata , quadratic palindromic system

Rights: Copyright © 2019 The Mathematical Society of the Republic of China

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Vol.23 • No. 6 • December, 2019
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