On highly efficient derivative-free family of numerical methods for solving polynomial equation simultaneously

A highly efficient new three-step derivative-free family of numerical iterative schemes for estimating all roots of polynomial equations is presented. Convergence analysis proved that the proposed simultaneous iterative method possesses 12th-order convergence locally. Numerical examples and computational cost are given to demonstrate the capability of the method presented.

Automated summary

This paper introduces a new numerical iterative scheme for estimating all roots of polynomial equations, which possesses 12th-order convergence locally according to convergence analysis. Numerical examples and computational cost are provided to demonstrate the capability of the proposed method.