A Solution of Inverse Eigenvalue Problems for Unitary Hessenberg Matrices

Numer. Math. J. Chinese Univ. (English Ser.)(English Ser.) 16 (2007), pp. 131-139

Published online: 2007-05

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@Article{NM-16-131,
author = {F. Li and L. Lin},
title = {A Solution of Inverse Eigenvalue Problems for Unitary Hessenberg Matrices},
journal = {Numerical Mathematics, a Journal of Chinese Universities},
year = {2007},
volume = {16},
number = {2},
pages = {131--139},
abstract = {
Let $H \in {\mathbb C}^{n\times n}$ be an $n
\times n $ unitary upper Hessenberg matrix whose subdiagonal
elements are all positive. Partition $H$ as
\begin{equation}\label{eq1}
H= \left [ \begin{array}{cc}
H_{11}&H_{12}\\
H_{21}&H_{22}
\end{array} \right ],
\end{equation}
where $H_{11}$ is its $k\times k$ leading principal submatrix;
$H_{22}$ is the complementary matrix of $H_{11}$. In this paper, $H
$ is constructed uniquely when its eigenvalues and the eigenvalues
of $\widehat{H}_{11}$ and $\widehat{H}_{22}$ are known. Here
$\widehat{H}_{11}$ and $\widehat{H}_{22}$ are rank-one modifications
of $ H_{11} $ and $H_{22}$ respectively.},
issn = {},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/nm/8051.html}
}

TY - JOUR
T1 - A Solution of Inverse Eigenvalue Problems for Unitary Hessenberg Matrices
AU - F. Li & L. Lin
JO - Numerical Mathematics, a Journal of Chinese Universities
VL - 2
SP - 131
EP - 139
PY - 2007
DA - 2007/05
SN - 16
DO - http://dor.org/
UR - https://global-sci.org/intro/article_detail/nm/8051.html
KW -
AB -
Let $H \in {\mathbb C}^{n\times n}$ be an $n
\times n $ unitary upper Hessenberg matrix whose subdiagonal
elements are all positive. Partition $H$ as
\begin{equation}\label{eq1}
H= \left [ \begin{array}{cc}
H_{11}&H_{12}\\
H_{21}&H_{22}
\end{array} \right ],
\end{equation}
where $H_{11}$ is its $k\times k$ leading principal submatrix;
$H_{22}$ is the complementary matrix of $H_{11}$. In this paper, $H
$ is constructed uniquely when its eigenvalues and the eigenvalues
of $\widehat{H}_{11}$ and $\widehat{H}_{22}$ are known. Here
$\widehat{H}_{11}$ and $\widehat{H}_{22}$ are rank-one modifications
of $ H_{11} $ and $H_{22}$ respectively.

F. Li & L. Lin. (1970). A Solution of Inverse Eigenvalue Problems for Unitary Hessenberg Matrices.

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*Numerical Mathematics, a Journal of Chinese Universities*.*16*(2). 131-139. doi: