Preprint 14-2017

Structured eigenvalue/eigenvector backward errors of matrix pencils arising in optimal control

Author(s) : Christian Mehl , Volker Mehrmann , Punit Sharma

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 14-2017

MSC 2000

65F15 Eigenvalues, eigenvectors

15A18 Eigenvalues, singular values, and eigenvectors

Abstract :
Eigenvalue and eigenpair backward errors are computed for matrix pencils arising in optimal control. In particular, formulas for backward errors are developed that are obtained under block-structure-preserving and symmetry-structure-preserving perturbations. It is shown that these eigenvalue and eigenpair backward errors are sometimes significantly larger than the corresponding backward errors that are obtained under perturbations that ignore the special structure of the pencil.

Keywords : Backward error, matrix pencil, optimal control, structured perturbation