New family of root-finding algorithms based on inverse rational interpolation

Abstract

Inverse interpolation with rational functions is investigated for the use in iterative refinement of the root approximation. A new family of optimal methods of arbitrary large order of convergence for solving nonlinear equations is presented. Experiments are conducted to check the influence of polynomial degrees in numerator and denominator on convergence properties of the proposed methods. Wolfram Mathematica 12 software was used to carry the computation due to its capabilities of arbitrary large precision arithmetic.