Condensed Forms for Skew-Hamiltonian/Hamiltonian Pencils

Numerical Computation of Deflating Subspaces of Skew-Hamiltonian/Hamiltonian Pencils

We discuss the numerical solution of structured generalized eigenvalue problems that arise from linear-quadratic optimal control problems, H∞ optimization, multibody systems, and many other areas of applied mathematics, physics, and chemistry. The classical approach for these problems requires computing invariant and deflating subspaces of matrices and matrix pencils with Hamiltonian and/or ske...

SLICOT Working Note 2013-3 MB04BV A FORTRAN 77 Subroutine to Compute the Eigenvectors Associated to the Purely Imaginary Eigenvalues of Skew-Hamiltonian/Hamiltonian Matrix Pencils

We implement a structure-preserving numerical algorithm for extracting the eigenvectors associated to the purely imaginary eigenvalues of skew-Hamiltonian/Hamiltonian matrix pencils. We compare the new algorithm with the QZ algorithm using random examples with di erent di culty. The results show that the new algorithm is signi cantly faster, more robust, and more accurate, especially for hard e...

Structure-Preserving Methods for Computing Eigenpairs of Large Sparse Skew-Hamiltonian/Hamiltonian Pencils

We study large, sparse generalized eigenvalue problems for matrix pencils, where one of the matrices is Hamiltonian and the other skew Hamiltonian. Problems of this form arise in the numerical simulation of elastic deformation of anisotropic materials, in structural mechanics and in the linear-quadratic control problem for partial diierential equations. We develop a structure-preserving skew-Ha...

Computational Experience with Structure-preserving Hamiltonian Solvers in Complex Spaces

Structure-preserving numerical techniques for computation of eigenvalues and stable deflating subspaces of complex skew-Hamiltonian/Hamiltonian matrix pencils, with applications in control systems analysis and design, are presented. The techniques use specialized algorithms to exploit the structure of such matrix pencils: the skew-Hamiltonian/Hamiltonian Schur form decomposition and the periodi...

Numerische Simulation Auf Massiv Parallelen Rechnern Structure-preserving Methods for Computing Eigenpairs of Large Sparse Skew-hamiltonian/hamiltonian Pencils Preprint-reihe Des Chemnitzer Sfb 393