Structured eigenvalue/eigenvector backward errors of matrix pencils arising in optimal control
Provides theoretical error analysis for structured matrix pencils in optimal control, but is incremental as it extends known backward error concepts to specific structures.
The paper develops formulas for eigenvalue and eigenvector backward errors of matrix pencils from optimal control, showing that structure-preserving perturbations can yield significantly larger backward errors than unstructured ones.
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.