On a cubically convergent derivative-free root finding method

Authors:
Miodrag S. Petkovic;Ljiljana D. Petkovic
Affiliations:
Faculty of Electronic Engineering, University of Nis, Nis, Serbia;Faculty of Mechanical Engineering, University of Nis, Nis, Serbia
Venue:
International Journal of Computer Mathematics
Year:
2007

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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.