Localization and Perturbations of Roots to Systems of Polynomial Equations

Michael Gil’ Department of Mathematics, Ben Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel Correspondence should be addressed to Michael Gil’, [email protected] Received 20 March 2012; Accepted 28 May 2012 Academic Editor: Andrei Volodin Copyright q 2012 Michael Gil’. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We establish estimates for the sums of absolute values of solutions of a zero-dimensional polynomial system. By these estimates, inequalities for the counting function of the roots are derived. In addition, bounds for the roots of perturbed systems are suggested.