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