Some topological and geometric properties of pseudozero set
Résumé
The pseudozero set of a polynomial p is the set of complex numbers that are roots of polynomials which are near to p. This is a powerful tool to analyze the sensitivity of roots with respect to perturbations of the coefficients. Some applications in algebraic computation and robust control theory have been proposed recently. In this paper, we establish some topological and geometric properties of the pseudozero set such as boundedness, compactness and convexity.