Approximate common divisors of polynomials and degree reduction for rational curves

摘要

This paper deals with how to perturb a given set of polynomials so as to include a common linear factor. An algorithm is derived for determining such a set of perturbation poly- nomials which are subject to certain constrains at the endpoints of a prescribed parametric inter- val and minimized in a certain sense. This result can be combined with subdivision technique to obtain a continuous piecewise approximation to a ration curve.