A new method for computing the stable invariant subspace of a real Hamiltonian matrix

DOI10.1016/S0377-0427(97)00146-5zbMath1005.65034MaRDI QIDQ1378991

Volker Mehrmann, Peter Benner, Hong-guo Xu

Publication date: 23 July 1998

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

algebraic Riccati equationeigenvalue problemerror analysisHamiltonian matrixQR algorithmLagrangian invariant subspacesymplectic URV decompositionbackward stable algorithmHamiltonian Schur form

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Matrix equations and identities (15A24) Hermitian, skew-Hermitian, and related matrices (15B57)

Related Items (17)

Some remarks on the complex \(J\)-symmetric eigenproblem ⋮ A numerical method for computing the Hamiltonian Schur form ⋮ An extended Hamiltonian QR algorithm ⋮ An invariant subspace method for large-scale algebraic Riccati equation ⋮ Structure Preserving Model Reduction of Parametric Hamiltonian Systems ⋮ An SVD-like matrix decomposition and its applications ⋮ Block circulant and Toeplitz structures in the linearized Hartree-Fock equation on finite lattices: tensor approach ⋮ Canonical forms for Hamiltonian and symplectic matrices and pencils ⋮ A generalized structured doubling algorithm for the numerical solution of linear quadratic optimal control problems ⋮ Perturbation analysis of the stochastic algebraic Riccati equation ⋮ A stabilization algorithm of the Navier–Stokes equations based on algebraic Bernoulli equation ⋮ Efficient methods for solving a nonsymmetric algebraic Riccati equation arising in stochastic fluid models ⋮ Hamilton and Jacobi come full circle: Jacobi algorithms for structured Hamiltonian eigenproblems ⋮ A structure-preserving method for positive realness problem in control ⋮ Numerical Linear Algebra Methods for Linear Differential-Algebraic Equations ⋮ A Core-Chasing Symplectic QR Algorithm ⋮ Numerical methods in control

Uses Software

• LAPACK
• Matlab
• LMI toolbox
• Control System Toolbox
• Robust Control Toolbox
• RICPAC

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Rang revealing QR factorizations
• On Hamiltonian and symplectic Hessenberg forms
• A divide and conquer method for unitary and orthogonal eigenproblems
• A Schur decomposition for Hamiltonian matrices
• A symplectic method for approximating all the eigenvalues of a Hamiltonian matrix
• The QR algorithm for unitary Hessenberg matrices
• The weak and strong stability of algorithms in numerical linear algebra
• A new look at the Lanczos algorithm for solving symmetric systems of linear equations
• The Riccati equation
• The autonomous linear quadratic control problem. Theory and numerical solution
• The matrix sign decomposition and its relation to the polar decomposition
• A multishift algorithm for the numerical solution of algebraic Riccati equations
• Matrix factorizations for symplectic QR-like methods
• Properties of a quadratic matrix equation and the solution of the continuous-time algebraic Riccati equation
• Correction to "Computation of supremal (A,B)-Invariant and controllability subspaces"
• Matrix Analysis
• A Hamiltonian $QR$ Algorithm
• The Sensitivity of the Stable Lyapunov Equation
• A Generalized Eigenvalue Approach for Solving Riccati Equations
• Linear model reduction and solution of the algebraic Riccati equation by use of the sign function†

This page was built for publication: A new method for computing the stable invariant subspace of a real Hamiltonian matrix