Bounding Zeros of Polynomial Systems Using B-Spline Expansionand Hansen-Sengupta Contractor

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 are proposing an algorithm to obtain 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 Hansen-Sengupta operator.

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