scholarly journals An inexact Cayley transform method for inverse eigenvalue problems

2004 ◽  
Vol 20 (5) ◽  
pp. 1675-1689 ◽  
Author(s):  
Zheng-Jian Bai ◽  
Raymond H Chan ◽  
Benedetta Morini
Keyword(s):  
Eigenvalue Problems ◽  
Cayley Transform ◽  
Transform Method ◽  
Inverse Eigenvalue Problems ◽  
Inverse Eigenvalue

An Ulm-like Cayley Transform Method for Inverse Eigenvalue Problems with Multiple Eigenvalues

2016 ◽  
Vol 9 (4) ◽  
pp. 664-685 ◽  
Author(s):  
Weiping Shen ◽  
Chong Li ◽  
Xiaoqing Jin
Keyword(s):  
Numerical Experiments ◽  
Eigenvalue Problems ◽  
Cayley Transform ◽  
Generalized Jacobian ◽  
Transform Method ◽  
Inverse Eigenvalue Problems ◽  
Multiple Eigenvalues ◽  
Inverse Eigenvalue ◽  
Quadratical Convergence ◽  
Approximate Jacobian

AbstractWe study the convergence of an Ulm-like Cayley transform method for solving inverse eigenvalue problems which avoids solving approximate Jacobian equations. Under the nonsingularity assumption of the relative generalized Jacobian matrices at the solution, a convergence analysis covering both the distinct and multiple eigenvalues cases is provided and the quadratical convergence is proved. Moreover, numerical experiments are given in the last section to illustrate our results.

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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