Safe starting regions by fixed points and tightening (Q1340881)

The paper deals with enclosure methods for finding all solutions of a system of nonlinear equations within a given box. In this context, `tightening' means a procedure which produces smaller boxes still containing all solutions via a guaranteed overestimation of the projections of the solution set to the faces of the box. A practical tightening algorithm for polynomial equations is presented. The tightening procedure is incorporated into a general iterative solution method involving bisection and a (non-) existence test based on the Krawczyk operator. The new method is tested against the method of \textit{E. Hansen} and \textit{S. Sengupta} [BIT 21, 201-211 (1981; Zbl 0455.65037)]. Numerical experiments for 10 different systems show the advantages of the new method.