For more general types of equations f (t) = 0, the problem of finding roots can be divided into two steps. First the roots must be isolated by finding intervals [ti , ti+1] which are known to contain one and only one root of the function. Secondly, the intervals about each root can be refined by reducing the size of the isolating interval until the root is located as accurately as possible usin...

‎In this paper a new family of fifteenth-order methods with high efficiency index is presented‎. This family include four evaluations of the function and one evaluation of its first derivative per iteration.‎ ‎Therefore‎, ‎this family of methods has the efficiency index which equals 1.71877‎. ‎In order to show the applicability and validity of the class‎, ‎some numerical examples are discussed‎.

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