Zero behavior in perturbed systems of polynomial equations / von Günther Hans Thallinger

• VerfasserIn: Thallinger, Günther Hans
• Place / Publishing House: 1998
• Year of Publication: 1998
• Language: English
• Physical Description: 80 Bl.

eng: If the data of a system of polynomial equations has only a limited accuracy, then the computation of the zero set (solution of the system) must be subject to small changes (perturbation) in the data. In this sense a system of polynomial equations whose zero set contains multiple zeros and/or zero manifolds is a degenerate case of a 0-dimensional polynomial system (set of polynomials which generate a 0-dimensional ideal), since upon a general perturbation a multiple zero or a zero manifold becomes a finite set of isolated simple zeros. These 0- dimensional polynomial systems pose severe difficulties to common localization procedures to analyze the behavior of multiple zeros and zero manifolds upon perturbations and present numerically stable localization algorithms.