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Volume 12, Issue 1
On Parameterised Quadratic Inverse Eigenvalue Problem

Meiling Xiang & Hua Dai

East Asian J. Appl. Math., 12 (2022), pp. 185-200.

Published online: 2021-10

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  • Abstract

It is shown that if prescribed eigenvalues are distinct, then the parameterised quadratic inverse eigenvalue problem is equivalent to a multiparameter eigenvalue problem. Moreover, a sufficient condition for the problem solvability is established. In order to find approximate solution of this problem, we employ the Newton method based on the smooth $QR$-decomposition with column pivoting and prove its locally quadratic convergence. Numerical examples illustrate the effectiveness of the method.

  • AMS Subject Headings

65F15

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COPYRIGHT: © Global Science Press

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@Article{EAJAM-12-185, author = {Xiang , Meiling and Dai , Hua}, title = {On Parameterised Quadratic Inverse Eigenvalue Problem}, journal = {East Asian Journal on Applied Mathematics}, year = {2021}, volume = {12}, number = {1}, pages = {185--200}, abstract = {

It is shown that if prescribed eigenvalues are distinct, then the parameterised quadratic inverse eigenvalue problem is equivalent to a multiparameter eigenvalue problem. Moreover, a sufficient condition for the problem solvability is established. In order to find approximate solution of this problem, we employ the Newton method based on the smooth $QR$-decomposition with column pivoting and prove its locally quadratic convergence. Numerical examples illustrate the effectiveness of the method.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.250321.230821}, url = {http://global-sci.org/intro/article_detail/eajam/19927.html} }
TY - JOUR T1 - On Parameterised Quadratic Inverse Eigenvalue Problem AU - Xiang , Meiling AU - Dai , Hua JO - East Asian Journal on Applied Mathematics VL - 1 SP - 185 EP - 200 PY - 2021 DA - 2021/10 SN - 12 DO - http://doi.org/10.4208/eajam.250321.230821 UR - https://global-sci.org/intro/article_detail/eajam/19927.html KW - Quadratic inverse eigenvalue problem, multiparameter eigenvalue problem, smooth $QR$-decomposition, Newton method. AB -

It is shown that if prescribed eigenvalues are distinct, then the parameterised quadratic inverse eigenvalue problem is equivalent to a multiparameter eigenvalue problem. Moreover, a sufficient condition for the problem solvability is established. In order to find approximate solution of this problem, we employ the Newton method based on the smooth $QR$-decomposition with column pivoting and prove its locally quadratic convergence. Numerical examples illustrate the effectiveness of the method.

Meiling Xiang & Hua Dai. (2021). On Parameterised Quadratic Inverse Eigenvalue Problem. East Asian Journal on Applied Mathematics. 12 (1). 185-200. doi:10.4208/eajam.250321.230821
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