A Preconditioned Riemannian Gauss-Newton Method for Least Squares Inverse Eigenvalue Problems
Abstract
This paper is concerned with the least squares inverse eigenvalue problem of reconstructing a linear parameterized real symmetric matrix from the prescribed partial eigenvalues in the sense of least squares, which was originally proposed by Chen and Chu [SIAM J. Numer. Anal., 33 (1996), pp. 2417--2430]. We provide a Riemannian inexact Gausss-Newton method for solving the least squares inverse eigenvalue problem. The global and local convergence analysis of the proposed method is discussed. Also, a preconditioned conjugate gradient method with an efficient preconditioner is proposed for solving the Riemannian Gauss-Newton equation. Finally, some numerical tests, including an application in the inverse Sturm-Liouville problem, are reported to illustrate the efficiency of the proposed method.
Cite
@article{arxiv.1806.06327,
title = {A Preconditioned Riemannian Gauss-Newton Method for Least Squares Inverse Eigenvalue Problems},
author = {Teng-Teng Yao and Zheng-Jian Bai and Xiao-Qing Jin and Zhi Zhao},
journal= {arXiv preprint arXiv:1806.06327},
year = {2018}
}
Comments
23 pages, 2 figures