The WY representation for products of householder matrices
SIAM Journal on Scientific and Statistical Computing - Papers from the Second Conference on Parallel Processing for Scientific Computin
A storage-efficient WY representation for products of householder transformations
SIAM Journal on Scientific and Statistical Computing
A set of level 3 basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
On a block implementation of Hessenberg multishift QR iteration
International Journal of High Speed Computing
Robust and optimal control
Matrix computations (3rd ed.)
A new method for computing the stable invariant subspace of a real Hamiltonian matrix
Journal of Computational and Applied Mathematics - Special issue: dedicated to William B. Gragg on the occasion of his 60th Birthday
On Pre-Conditioning of Matrices
Journal of the ACM (JACM)
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
ACM Transactions on Mathematical Software (TOMS)
Parallel Algorithms for Numerical Linear Algebra
Parallel Algorithms for Numerical Linear Algebra
Symplectic Balancing of Hamiltonian Matrices
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
The Quadratic Eigenvalue Problem
SIAM Review
Numerical Solution of Quadratic Eigenvalue Problems with Structure-Preserving Methods
SIAM Journal on Scientific Computing
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
Handbook for Automatic Computation: Linear Algebra (Grundlehren Der Mathematischen Wissenschaften, Vol 186)
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This article describes Fortran 77 subroutines for computing eigenvalues and invariant subspaces of Hamiltonian and skew-Hamiltonian matrices. The implemented algorithms are based on orthogonal symplectic decompositions, implying numerical backward stability as well as symmetry preservation for the computed eigenvalues. These algorithms are supplemented with balancing and block algorithms which can lead to considerable accuracy and performance improvements. As a by-product, an efficient implementation for computing symplectic QR decompositions is provided. We demonstrate the usefulness of the subroutines for several, practically relevant examples.