scholarly journals On uniqueness theorems for second order inverse eigenvalue problems

1986 ◽  
Vol 118 (1) ◽  
pp. 38-41 ◽  
Author(s):  
Joyce R McLaughlin
Keyword(s):  
Eigenvalue Problems ◽  
Second Order ◽  
Uniqueness Theorems ◽  
Inverse Eigenvalue Problems ◽  
Inverse Eigenvalue

scholarly journals The Robust Pole Assignment Problem for Second-Order Systems

2010 ◽  
Vol 2010 ◽  
pp. 1-13
Author(s):  
Hao Liu
Keyword(s):  
Assignment Problem ◽  
Optimization Problem ◽  
Eigenvalue Problems ◽  
Pole Assignment ◽  
Second Order ◽  
Assignment Problems ◽  
Inverse Eigenvalue Problems ◽  
Quadratic Pencil ◽  
Inverse Eigenvalue ◽  
Second Order Systems

Pole assignment problems are special algebraic inverse eigenvalue problems. In this paper, we research numerical methods of the robust pole assignment problem for second-order systems. The problem is formulated as an optimization problem. Depending upon whether the prescribed eigenvalues are real or complex, we separate the discussion into two cases and propose two algorithms for solving this problem. Numerical examples show that the problem of the robust eigenvalue assignment for the quadratic pencil can be solved effectively.

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.

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
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