The Computer Implementations of an Efficient Iterative Algorithm Based on the Inverse Newton Interpolation

In this work, we develop a simple yet practical algorithm for solving nonlinear optimization problems by finding a root of a real function f'(x)=0 with a good local convergence. The algorithm uses an inverse interpolation method that can be easily implemented in software packages for achieving desired convergence orders. For the general n-point formula, the order of convergence rate of the presented algorithm is τ_n, the unique positive root of the equation xⁿ - x^(n-1)-...-x-1=0.