full
search.png

Search

close.png

Cancel

arrow
Volume 12, Issue 1
On Parameterised Quadratic Inverse Eigenvalue Problem

Meiling Xiang & Hua Dai

DOI: 10.4208/eajam.250321.230821

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

Published online: 2021-10

Preview Full PDF 3022 42968

Cited by

google scholar semantic scholar
Export citation
  • 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.

  • Keywords

Quadratic inverse eigenvalue problem, multiparameter eigenvalue problem, smooth $QR$-decomposition, Newton method.

  • AMS Subject Headings

65F15

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@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.

Xiang , Meiling and Dai , Hua. (2021). On Parameterised Quadratic Inverse Eigenvalue Problem. East Asian Journal on Applied Mathematics. 12 (1). 185-200. doi:10.4208/eajam.250321.230821
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard