On a cubically convergent derivative-free root finding method

Abstract

Using a method for accelerating convergence and Weierstrass’ correction, a cubically convergent method without derivatives for the simultaneous determination of polynomial zeros is derived. The proposed method possesses approximately the structure of Halley's method. Using the Gauss–Seidel approach, the single-step method is outlined. Convergence analysis and computational aspects are reported.

Keywords:

• Zero-finding methods
• Simultaneous methods
• Polynomial zeros
• Convergence rate

Acknowledgements

The authors greatly appreciate the valuable comments and suggestions of the referees. This work was supported by the Serbian Ministry of Science under grant 144024.