A free-derivative iteration method of order three having convergence of both point and interval for nonlinear equations
A new iterative formulae containing only the values of a nonlinear function \(f\) is proposed to compute the both sequences, \(\{ x_n\}\) and \(\{[a_n,b_n]\}\), converging cubically to the unique zero of \(f\). The numerical results show that the proposed algorithm leads to solution in certain cases where the Newton or Steffensen method fails.
scientific article; zbMATH DE number 1977923