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Eigenvalue and eigenpair backward errors are computed for matrix pencilsarising in optimal control. In particular, formulas for backward errors aredeveloped that are obtained under block-structure-preserving andsymmetry-structure-preserving perturbations. It is shown that these eigenvalueand eigenpair backward errors are sometimes significantly larger than thecorresponding backward errors that are obtained under perturbations that ignorethe special structure of the pencil.

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