A correction note on "New iterative schemes for nonlinear equations"

TL;DR

This paper corrects a previous claim by demonstrating that a proposed iterative scheme for nonlinear equations does not achieve cubic convergence as initially claimed.

Contribution

It provides a correction to Noor's 2007 work by showing that the algorithm does not have cubic convergence, clarifying the true convergence rate.

Findings

Algorithm 2.4 is not cubically convergent

The original proof of cubic convergence was incorrect

Clarifies the actual convergence properties of the algorithm

Abstract

In Noor (2007)[Muhammad Aslam Noor, New iterative schemes for nonlinear equations, Appl. Math. Comput. 187 (2007) 937-943], proposed an algorithm namely \textbf{Algorithm 2.4} and established a proof to show cubic convergence. The presented proof is wrong. In this article, we show that \textbf{Algorithm 2.4} is not cubically convergent.