A numerical method for computing the Hamiltonian Schur form
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Publication:861657
DOI10.1007/s00211-006-0043-0zbMath1116.65043OpenAlexW1995028404MaRDI QIDQ861657
Xinmin Liu, Delin Chu, Volker Mehrmann
Publication date: 30 January 2007
Published in: Numerische Mathematik (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00211-006-0043-0
algorithmHamiltonian matrixRiccati matrix equationbackward stabilitystructured Schur formsymplectic URV-decomposition
Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Multivariable systems, multidimensional control systems (93C35)
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Cites Work
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- On Hamiltonian and symplectic Hessenberg forms
- Computing the CS and the generalized singular value decompositions
- On the reduction of a Hamiltonian matrix to Hamiltonian Schur form
- A Schur decomposition for Hamiltonian matrices
- A symplectic method for approximating all the eigenvalues of a Hamiltonian matrix
- Three methods for refining estimates of invariant subspaces
- The weak and strong stability of algorithms in numerical linear algebra
- The autonomous linear quadratic control problem. Theory and numerical solution
- Simultaneous iteration for computing invariant subspaces of non-Hermitian matrices
- A note on the numerical solution of complex Hamiltonian and skew-Hamiltonian eigenvalue problems
- A multishift algorithm for the numerical solution of algebraic Riccati equations
- A numerically stable, structure preserving method for computing the eigenvalues of real Hamiltonian or symplectic pencils
- A new method for computing the stable invariant subspace of a real Hamiltonian matrix
- Matrix Riccati equations in control and systems theory
- Perturbation analysis for the eigenvalue problem of a formal product of matrices
- Properties of a quadratic matrix equation and the solution of the continuous-time algebraic Riccati equation
- Structure-Preserving Methods for Computing Eigenpairs of Large Sparse Skew-Hamiltonian/Hamiltonian Pencils
- Perturbation Analysis of Hamiltonian Schur and Block-Schur Forms
- Existence, Uniqueness, and Parametrization of Lagrangian Invariant Subspaces
- Topological Semiconjugacy of Piecewise Monotone Maps of the Interval
- Algorithm 854
- A Hamiltonian $QR$ Algorithm
- A Schur method for solving algebraic Riccati equations
- A Generalized Eigenvalue Approach for Solving Riccati Equations
- Numerical solution of the discrete-time periodic Riccati equation
- A symplectic QR like algorithm for the solution of the real algebraic Riccati equation
- Perturbation Bounds for Isotropic Invariant Subspaces of Skew-Hamiltonian Matrices
- Linear Perturbation Theory for Structured Matrix Pencils Arising in Control Theory