Pseudozeros are useful to describe how perturbations of polynomial
coefficients affect its zeros. We compare two types of pseudozero
sets: the complex and the real pseudozero sets.
These sets differ with respect to the type of perturbations.
The first set – complex perturbations of a complex polynomial – has been
intensively studied while the second one – real perturbations of a real
polynomial – seems to have received little attention.
We present a computable formula for the real pseudozero set and a
comparison between these two pseudozero sets. We conclude that the
complex pseudozero sets have to be preferred except when the perturbed
real polynomials admit non-real zeros. We also give some applications
of pseudozero set in control theory.