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arXiv · 1806.06327

A Preconditioned Riemannian Gauss-Newton Method for Least Squares Inverse Eigenvalue Problems

Teng-Teng Yao·Zheng-Jian Bai·Xiao-Qing Jin·Zhi Zhao
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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.

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Teng-Teng Yao, Zheng-Jian Bai, Xiao-Qing Jin, Zhi Zhao. 2018-06-17. A Preconditioned Riemannian Gauss-Newton Method for Least Squares Inverse Eigenvalue Problems. https://arxiv.org/abs/1806.06327

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