Subdivision Algorithms for Solving a Polynomial System: Empirical Comparisons

Abstract

This paper deals with the methods based on subdivision for the solution of systems of nonlinear polynomial equations. We compare the performance of interval arithmetic based predicates with its polynomial B-spline form based predicates for the Newton, Hansen-Sengupta, and Krawczyk contractor.

          The proposed algorithms of polynomial B-spline forms predicates for obtaining the solutions of polynomial system, is based on following technique:

1) transformation of the original nonlinear algebraic equations into polynomial B-spline form; 2) includes a pruning step using polynomial B-spline predicate.

          We solved two numerical examples with proposed algorithms. The performance of proposed algorithms is compared with INTLAB solver based predicates. In algorithm suggested the value of polynomial B-spline predicate is obtained from B-spline coefficient. This approach avoids the repeated computation of function value and the derivative is directly obtained using B-spline coefficients.