Polynomial Equations in Geometric Modeling and the Control of Vibrations in Manufacturing

The need to compute the roots of a polynomial arises in the determination of the points of intersection of curves and surfaces and the control of vibrations during machining of a component. Few problems arise if the roots are simple and well separated, but the reliable computation of multiple roots is significantly more difficult because of their ill-posed nature. Even if the exact form of a polynomial has multiple roots, an inexact form of the polynomial has, with probability almost one, simple roots. This presentation shows how to reliably compute multiple roots of the exact polynomial given an inexact form of the polynomial, retaining a fundamental property of the theoretically exact polynomial in the computed roots.