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BIT Numerical Mathematics

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09-01-2020

A geometric Gauss–Newton method for least squares inverse eigenvalue problems

Authors: Teng-Teng Yao, Zheng-Jian Bai, Xiao-Qing Jin, Zhi Zhao

Published in: BIT Numerical Mathematics | Issue 3/2020

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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 33:2417–2430, 1996). We provide a geometric Gauss–Newton method for solving the least squares inverse eigenvalue problem. The global and local convergence analysis of the proposed method is established under some assumptions. Also, a preconditioned conjugate gradient method with an efficient preconditioner is proposed for solving the geometric 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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Title: A geometric Gauss–Newton method for least squares inverse eigenvalue problems
Authors: Teng-Teng Yao
Zheng-Jian Bai
Xiao-Qing Jin
Zhi Zhao
Publication date: 09-01-2020
Publisher: Springer Netherlands
Published in: BIT Numerical Mathematics / Issue 3/2020
Print ISSN: 0006-3835
Electronic ISSN: 1572-9125
DOI: https://doi.org/10.1007/s10543-019-00798-9

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