  First, we derive explicit computable expressions of structured backward
errors of approximate eigenelements of structured matrix polynomials including
symmetric, skew-symmetric, Hermitian, skew-Hermitian, even and odd polynomials.
We also determine minimal structured perturbations for which approximate
eigenelements are exact eigenelements of the perturbed polynomials. Next, we
analyze the effect of structure preserving linearizations of structured matrix
polynomials on the structured backward errors of approximate eigenelements. We
identify structure preserving linearizations which have almost no adverse
effect on the structured backward errors of approximate eigenelements of the
polynomials. Finally, we analyze structured pseudospectra of a structured
matrix polynomial and establish a partial equality between unstructured and
structured pseudospectra.
