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

Abstract

Abstract 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.

Keywords

• Numerical scheme
• Polynomials
• Computational efficiency
• CPU-time
• Convergence order