An efficient and stable structure preserving algorithm for computing the eigenvalues of a Hamiltonian matrix

DOI10.1007/BF02439460zbMath1143.65333MaRDI QIDQ1400073

Qingyou Yan, Xiwen Xiong

Publication date: 13 August 2003

Published in: Applied Mathematics and Mechanics. (English Edition) (Search for Journal in Brave)

zbMATH Keywords

stabilityeigenvalueHamiltonian matrixbacktrack techniquedisunstabilizationQR like algorithmratio-reduction

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A symplectic method for approximating all the eigenvalues of a Hamiltonian matrix
• A new method for computing the closed-loop eigenvalues of a discrete-time algebraic Riccati equation
• An iterative algorithm for the solution of the discrete-time algebraic Riccati equation
• On computing the eigenvalues of a symplectic pencil
• An implicitly restarted symplectic Lanczos method for the Hamiltonian eigenvalue problem
• A numerically stable, structure preserving method for computing the eigenvalues of real Hamiltonian or symplectic pencils
• A Hamiltonian $QR$ Algorithm
• A Symplectic Orthogonal Method for Single Input or Single Output Discrete Time Optimal Quadratic Control Problems
• On the numerical solution of the discrete-time algebraic Riccati equation
• A Chart of Numerical Methods for Structured Eigenvalue Problems
• Computation of Stable Invariant Subspaces of Hamiltonian Matrices
• Numerical solution of the discrete-time periodic Riccati equation
• On Computing Stable Lagrangian Subspaces of Hamiltonian Matrices and Symplectic Pencils
• A symplectic QR like algorithm for the solution of the real algebraic Riccati equation