Structured eigenvalue backward errors for rational matrix functions with symmetry structures.

We derive computable formulas for the structured backward errors of a complex number λ when considered as an approximate eigenvalue of rational matrix functions that carry a symmetry structure. We consider symmetric, skew-symmetric, Hermitian, skew-Hermitian, ∗ -palindromic, T-even, T-odd, ∗ -even, and ∗ -odd structures. Numerical experiments show that the backward errors with respect to structure-preserving and arbitrary perturbations are significantly different. [ABSTRACT FROM AUTHOR]