Numerical Computation of Deflating Subspaces of 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...

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...

On reducing and deflating subspaces of matrices

A multilinear approach based on Grassmann representatives and matrix compounds is presented for the identification of reducing pairs of subspaces that are common to two or more matrices. Similar methods are employed to characterize the deflating pairs of subspaces for a regular matrix pencil A+ sB, namely, pairs of subspaces (L,M) such that AL ⊆ M and BL ⊆ M.

Condensed Forms for Skew-Hamiltonian/Hamiltonian Pencils

Abstract In this paper we consider real or complex skew-Hamiltonian/Hamiltonian pencils λS −H, i.e., pencils where S is a skew-Hamiltonian and H is a Hamiltonian matrix. These pencils occur for example in the theory of continuous time, linear quadratic optimal control problems. We reduce these pencils to canonical and Schur-type forms under structure-preserving transformations, i.e., J-congruen...

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