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

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...

FORTRAN 77 Subroutines for the Solution of Skew-Hamiltonian/Hamiltonian Eigenproblems - Part II: Implementation and Numerical Results

Skew-Hamiltonian/Hamiltonian matrix pencils λS −H appear in many applications, including linear quadratic optimal control problems, H∞-optimization, certain multi-body systems and many other areas in applied mathematics, physics, and chemistry. In these applications it is necessary to compute certain eigenvalues and/or corresponding deflating subspaces of these matrix pencils. Recently develope...

Robust numerical methods for robust control

We present numerical methods for the solution of the optimal H∞ control problem. In particular, we investigate the iterative part often called the γ-iteration. We derive a method with better robustness in the presence of rounding errors than other existing methods. It remains robust in the presence of rounding errors even as γ approaches its optimal value. For the computation of a suboptimal co...

Numerical Solution of Quadratic Eigenvalue Problems with Structure-Preserving Methods

Numerical methods for the solution of large scale structured quadratic eigenvalue problems are discussed. We describe a new extraction procedure for the computation of eigenvectors and invariant subspaces of skew-Hamiltonian/Hamiltonian pencils using the recently proposed skew-Hamiltonian isotropic implicitly restarted Arnoldi method (SHIRA). As an application we discuss damped gyroscopic syste...

Numerische Simulation Auf Massiv Parallelen Rechnern Numerical Computation of Deeating Subspaces of Embedded Hamiltonian Pencils Preprint-reihe Des Chemnitzer Sfb 393