B-Spline Krawczyk Approach for Solving Polynomial Systems

Abstract

Engineering applications such as computer-aided design, robotics, and electrical network requires an efficient computational technique of finding all roots of a system of nonlinear polynomial equations in s variables which lie within an s dimensional box. We propose an algorithm for obtaining the roots of the polynomial system, it is based on the following technique: (1) transformation of the original nonlinear algebraic equations into polynomial B-spline form; (2) includes a pruning step using B-spline Krawczyk operator.

We compare the performance of the proposed B-spline Krawczyk operator with that of Interval Krawczyk operator using numerical examples, providing the superiority of the proposed approach.