A study on new computational local orders of convergence
This work provides practical tools for estimating convergence order without the root, benefiting numerical analysts working on iterative methods.
The paper introduces four new variants of the Computational Order of Convergence (COC) for one-point iterative methods with memory, which do not require knowledge of the root, and demonstrates their accuracy through numerical experiments with adaptive arithmetic.
Four new variants of the Computational Order of Convergence (COC) of a one-point iterative method with memory for solving nonlinear equations are presented. Furthermore, the way to approximate the new variants to the local order of convergence is analyzed. Three of the new definitions given here do not involve the unknown root. Numerical experiments using adaptive arithmetic with multiple precision and a stopping criteria are implemented without using any known root.