The Riemannian two-step perturbed Gauss–Newton method for least squares inverse eigenvalue problems

2021 ◽  
pp. 113971
Author(s):  
Zhi Zhao ◽  
Xiao-Qing Jin ◽  
Teng-Teng Yao
Keyword(s):  
Least Squares ◽  
Newton Method ◽  
Eigenvalue Problems ◽  
Inverse Eigenvalue Problems ◽  
Inverse Eigenvalue

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

2020 ◽  
Vol 60 (3) ◽  
pp. 825-852 ◽  
Author(s):  
Teng-Teng Yao ◽  
Zheng-Jian Bai ◽  
Xiao-Qing Jin ◽  
Zhi Zhao
Keyword(s):  
Least Squares ◽  
Newton Method ◽  
Eigenvalue Problems ◽  
Inverse Eigenvalue Problems ◽  
Inverse Eigenvalue

scholarly journals A Generalized Inexact Newton Method for Inverse Eigenvalue Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Weiping Shen
Keyword(s):  
Newton Method ◽  
Quadratic Convergence ◽  
Eigenvalue Problems ◽  
Generalized Newton Method ◽  
Inexact Newton Method ◽  
Numerical Tests ◽  
Inverse Eigenvalue Problems ◽  
Inverse Eigenvalue ◽  
Generalized Newton ◽  
Special Case

We propose a generalized inexact Newton method for solving the inverse eigenvalue problems, which includes the generalized Newton method as a special case. Under the nonsingularity assumption of the Jacobian matrices at the solutionc*, a convergence analysis covering both the distinct and multiple eigenvalue cases is provided and the quadratic convergence property is proved. Moreover, numerical tests are given in the last section and comparisons with the generalized Newton method are made.

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