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Volume 12, Issue 2
Smallest Singular Value Based Newton-Like Methods for Solving Quadratic Inverse Eigenvalue Problem

Meiling Xiang & Hua Dai

DOI: 10.4208/eajam.020921.251121

East Asian J. Appl. Math., 12 (2022), pp. 333-352.

Published online: 2022-02

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  • Abstract

A Newton method for solving quadratic inverse eigenvalue problems is proposed. The method is based on the properties of the smallest singular value of a matrix. In order to reduce computational cost, we use approximations of the smallest singular value and the corresponding unit left and right singular vectors obtained by the one-step inverse iteration. It is shown that both the proposed method and its modification have locally quadratic convergence. Numerical results confirm theoretical findings and demonstrate the effectiveness of the methods proposed.

  • Keywords

Quadratic inverse eigenvalue problem, Newton method, Newton-like method, singular value, singular vector.

  • AMS Subject Headings

15A29, 65F18

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-12-333, author = {Xiang , Meiling and Dai , Hua}, title = {Smallest Singular Value Based Newton-Like Methods for Solving Quadratic Inverse Eigenvalue Problem}, journal = {East Asian Journal on Applied Mathematics}, year = {2022}, volume = {12}, number = {2}, pages = {333--352}, abstract = {

A Newton method for solving quadratic inverse eigenvalue problems is proposed. The method is based on the properties of the smallest singular value of a matrix. In order to reduce computational cost, we use approximations of the smallest singular value and the corresponding unit left and right singular vectors obtained by the one-step inverse iteration. It is shown that both the proposed method and its modification have locally quadratic convergence. Numerical results confirm theoretical findings and demonstrate the effectiveness of the methods proposed.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.020921.251121}, url = {http://global-sci.org/intro/article_detail/eajam/20257.html} }
TY - JOUR T1 - Smallest Singular Value Based Newton-Like Methods for Solving Quadratic Inverse Eigenvalue Problem AU - Xiang , Meiling AU - Dai , Hua JO - East Asian Journal on Applied Mathematics VL - 2 SP - 333 EP - 352 PY - 2022 DA - 2022/02 SN - 12 DO - http://doi.org/10.4208/eajam.020921.251121 UR - https://global-sci.org/intro/article_detail/eajam/20257.html KW - Quadratic inverse eigenvalue problem, Newton method, Newton-like method, singular value, singular vector. AB -

A Newton method for solving quadratic inverse eigenvalue problems is proposed. The method is based on the properties of the smallest singular value of a matrix. In order to reduce computational cost, we use approximations of the smallest singular value and the corresponding unit left and right singular vectors obtained by the one-step inverse iteration. It is shown that both the proposed method and its modification have locally quadratic convergence. Numerical results confirm theoretical findings and demonstrate the effectiveness of the methods proposed.

Xiang , Meiling and Dai , Hua. (2022). Smallest Singular Value Based Newton-Like Methods for Solving Quadratic Inverse Eigenvalue Problem. East Asian Journal on Applied Mathematics. 12 (2). 333-352. doi:10.4208/eajam.020921.251121
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