Nonunitary algorithms for real Hamiltonian or real symplectic eigenvalue problems

2006 ◽  
pp. 131-139
Keyword(s):  
Eigenvalue Problems ◽  
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.

scholarly journals New analytic bending, buckling, and free vibration solutions of rectangular nanoplates by the symplectic superposition method

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Xinran Zheng ◽  
Mingqi Huang ◽  
Dongqi An ◽  
Chao Zhou ◽  
Rui Li
Keyword(s):  
Hamiltonian System ◽  
Free Vibration ◽  
Eigenvalue Problems ◽  
Analytic Solutions ◽  
Symplectic Space ◽  
Superposition Method ◽  
Mathematical Solution ◽  
Simply Supported ◽  
Solution Methods ◽  
Symplectic Eigenvalue

AbstractNew analytic bending, buckling, and free vibration solutions of rectangular nanoplates with combinations of clamped and simply supported edges are obtained by an up-to-date symplectic superposition method. The problems are reformulated in the Hamiltonian system and symplectic space, where the mathematical solution framework involves the construction of symplectic eigenvalue problems and symplectic eigen expansion. The analytic symplectic solutions are derived for several elaborated fundamental subproblems, the superposition of which yields the final analytic solutions. Besides Lévy-type solutions, non-Lévy-type solutions are also obtained, which cannot be achieved by conventional analytic methods. Comprehensive numerical results can provide benchmarks for other solution methods.

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