Real Root Approximation Using Fat Spheres

We present a new algorithm to approximate real roots of multivariate polynomial systems. This algorithm combines the standard subdivision technique with a new domain reduction strategy. We introduce fat spheres as multidimensional quadratic enclosures for algebraic hypersurfaces. Then we present a local reformulation technique of the algebraic system, which provides a method to generate fat spheres. Based on the fat sphere generation we formulate the new domain reduction strategy. The iterative domain reduction generates a sequence of bounding boxes, which converge with order three to the single roots of a multivariate polynomial system.