SIAM Journal on Scientific and Statistical Computing
On the numerical properties of the schur approach for solving the matrix Riccati equation
Systems & Control Letters
An extended set of FORTRAN basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
The algebraic eigenvalue problem
The algebraic eigenvalue problem
A set of level 3 basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
A fast algorithm to computer the H∞ -norm of a transfer function matrix
Systems & Control Letters
A stability-enhancing scaling procedure for Schur-Riccati solvers
Systems & Control Letters
LAPACK's user's guide
Forward instability of tridiagonal QR
SIAM Journal on Matrix Analysis and Applications
Computation of Stable Invariant Subspaces of Hamiltonian Matrices
SIAM Journal on Matrix Analysis and Applications
Matrix computations (3rd ed.)
A Stabilized Matrix Sign Function Algorithm for Solving Algebraic Riccati Equations
SIAM Journal on Scientific Computing
Basic Linear Algebra Subprograms for Fortran Usage
ACM Transactions on Mathematical Software (TOMS)
Hamiltonian and symplectic algorithms for the algebraic riccati equation
Hamiltonian and symplectic algorithms for the algebraic riccati equation
Structure preservation: a challenge in computational control
Future Generation Computer Systems - Selected papers on theoretical and computational aspects of structural dynamical systems in linear algebra and control
On the computation of few eigenvalues of positive definite Hamiltonian matrices
Future Generation Computer Systems
Algorithm 854: Fortran 77 subroutines for computing the eigenvalues of Hamiltonian matrices II
ACM Transactions on Mathematical Software (TOMS)
On the computation of few eigenvalues of positive definite Hamiltonian matrices
Future Generation Computer Systems
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This article describes LAPACK-based Fortran 77 subroutines for the reduction of a Hamiltonian matrix to square-reduced form and the approximation of all its eigenvalues using the implicit version of Van Loan's method. The transformation of the Hamiltonian matrix to a square-reduced form transforms a Hamiltonian eigenvalue problem of order 2n to a Hessenberg eigenvalue problem of order n. The eigenvalues of the Hamiltonian matrix are the square roots of those of the Hessenberg matrix. Symplectic scaling and norm scaling are provided, which, in some cases, improve the accuracy of the computed eigenvalues. We demonstrate the performance of the subroutines for several examples and show how they can be used to solve some control-theoretic problems.