Renormalized oscillation theory for symplectic eigenvalue problems with nonlinear dependence on the spectral parameter

2020 ◽  
Vol 26 (4) ◽  
pp. 458-487
Author(s):  
Julia Elyseeva
Keyword(s):  
Spectral Parameter ◽  
Eigenvalue Problems ◽  
Oscillation Theory ◽  
Nonlinear Dependence ◽  
Symplectic Eigenvalue

Backward Error Analysis for Eigenproblems Involving Conjugate Symplectic Matrices

2015 ◽  
Vol 5 (4) ◽  
pp. 312-326 ◽  
Author(s):  
Wei-wei Xu ◽  
Wen Li ◽  
Xiao-qing Jin
Keyword(s):  
Optimal Control Problems ◽  
Eigenvalue Problems ◽  
Backward Error Analysis ◽  
Linear Quadratic ◽  
Backward Error ◽  
Linear Quadratic Optimal Control ◽  
Quadratic Optimal Control ◽  
Symplectic Eigenvalue ◽  
Backward Errors ◽  
Symplectic Matrices

AbstractConjugate symplectic eigenvalue problems arise in solving discrete linear-quadratic optimal control problems and discrete algebraic Riccati equations. In this article, backward errors of approximate pairs of conjugate symplectic matrices are obtained from their properties. Several numerical examples are given to illustrate the results.

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