Volume 4, Issue 1
General Solutions for a Class of Inverse Quadratic Eigenvalue Problems

Xiaoqin Tan & Li Wang

East Asian J. Appl. Math., 4 (2014), pp. 69-81.

Published online: 2018-02

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  • Abstract

Based on various matrix decompositions, we compare different techniques for solving the inverse quadratic eigenvalue problem, where $n×n$ real symmetric matrices $M$, $C$ and $K$ are constructed so that the quadratic pencil $Q(λ) = λ^{2}M+λC+K$ yields good approximations for the given $k$ eigenpairs. We discuss the case where $M$ is positive definite for $1≤ k≤n$, and a general solution to this problem for $n+1≤k≤2n$. The efficiency of our methods is illustrated by some numerical experiments.

  • Keywords

Quadratic eigenvalue problem, inverse quadratic eigenvalue problem, partially prescribed spectral information.

  • AMS Subject Headings

65F18

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-4-69, author = {}, title = {General Solutions for a Class of Inverse Quadratic Eigenvalue Problems}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {4}, number = {1}, pages = {69--81}, abstract = {

Based on various matrix decompositions, we compare different techniques for solving the inverse quadratic eigenvalue problem, where $n×n$ real symmetric matrices $M$, $C$ and $K$ are constructed so that the quadratic pencil $Q(λ) = λ^{2}M+λC+K$ yields good approximations for the given $k$ eigenpairs. We discuss the case where $M$ is positive definite for $1≤ k≤n$, and a general solution to this problem for $n+1≤k≤2n$. The efficiency of our methods is illustrated by some numerical experiments.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.100413.021013a}, url = {http://global-sci.org/intro/article_detail/eajam/10822.html} }
TY - JOUR T1 - General Solutions for a Class of Inverse Quadratic Eigenvalue Problems JO - East Asian Journal on Applied Mathematics VL - 1 SP - 69 EP - 81 PY - 2018 DA - 2018/02 SN - 4 DO - http://doi.org/10.4208/eajam.100413.021013a UR - https://global-sci.org/intro/article_detail/eajam/10822.html KW - Quadratic eigenvalue problem, inverse quadratic eigenvalue problem, partially prescribed spectral information. AB -

Based on various matrix decompositions, we compare different techniques for solving the inverse quadratic eigenvalue problem, where $n×n$ real symmetric matrices $M$, $C$ and $K$ are constructed so that the quadratic pencil $Q(λ) = λ^{2}M+λC+K$ yields good approximations for the given $k$ eigenpairs. We discuss the case where $M$ is positive definite for $1≤ k≤n$, and a general solution to this problem for $n+1≤k≤2n$. The efficiency of our methods is illustrated by some numerical experiments.

Xiaoqin Tan & Li Wang. (1970). General Solutions for a Class of Inverse Quadratic Eigenvalue Problems. East Asian Journal on Applied Mathematics. 4 (1). 69-81. doi:10.4208/eajam.100413.021013a
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