.svg){kind=logo}
INVERSE EIGENVALUE PROBLEM FOR SYMMETRIC MATRICES IN THE CONTEXT OF THE LIE GROUP $SO(n)$
Keywords:
inverse eigenvalue problem, symmetric matrices, Lie group $SO(n)$, linearizationDOI:
https://doi.org/10.17654/0972555524015Abstract
In this paper, a new approach to the solution of the inverse eigenvalue problem for symmetric matrices is obtained by means of linearization of the Lie group $SO(n)$. The method formulated is motivated by an earlier approach which used classical Newton’s method to solve inverse eigenvalue problem for symmetric matrices. In both the cases, initialization of the iteration is implemented utilizing a related singular symmetric matrix. Numerical illustration for the case of $2 \times 2$ symmetric matrices is presented. Comparing the results of the computation, it was found that the two methods were in agreement.
Received: December 10, 2023
Accepted: March 1, 2024
References
Francis T. Oduro, Solution of the inverse eigenvalue problem for certain (anti-) Hermitian matrices using Newton’s method, Journal of Mathematics Research 6(2) (2014), 64-71.
Emmanuel Akweittey, Kwasi Baah Gyamfi and Gabriel Obed Fosu, Solubility existence of inverse eigenvalue problem for a class of singular Hermitian matrices, Journal of Mathematics and System Science 9 (2019), 119-123.
Daniel Boley and Gene H. Golub, A survey of matrix inverse eigenvalue problems, Inverse Problems 3(4) (1987), 595.
Jing Cai and Jianlong Chen, Least-squares solutions of generalized inverse eigenvalue problem over Hermitian-Hamiltonian matrices with a submatrix constraint, Computational and Applied Mathematics 37(1) (2018), 593-603.
Anthony G. Cronin and Thomas J. Laffey, The diagonalizable nonnegative inverse eigenvalue problem, Special Matrices 6(1) (2018), 273-281.
Charles R. Johnson, Carlos Marijuán and Miriam Pisonero, Ruling out certain 5-spectra for the symmetric nonnegative inverse eigenvalue problem, Linear Algebra and its Applications 512 (2017), 129-135.
Xia Ji, Jiguang Sun and Hehu Xie, A multigrid method for Helmholtz transmission eigenvalue problems, Journal of Scientific Computing 60(2) (2014), 276-294.
K. B. Gyamfi, Solution of inverse eigenvalue problem of certain singular Hermitian matrices, Ph. D. Thesis, Kwame Nkrumah University of Science and Technology, Kumasi, 2012.
Downloads
Published
Issue
Section
License
Copyright (c) 2024 PUSHPA PUBLISHING HOUSE, PRAYAGRAJ, INDIA
This work is licensed under a Creative Commons Attribution 4.0 International License.
_________________________________
Attribution: Credit Pusha Publishing House as the original publisher, including title and author(s) if applicable.
Non-Commercial Use: For non-commercial purposes only. No commercial activities without explicit permission.
No Derivatives: Modifying or creating derivative works not allowed without written permission.
Contact Pusha Publishing House for more info or permissions.
