On convergence of a new secant-like method for solving nonlinear equations

摘要

In this paper, we prove that the order of a new secant-like method presented recently with the so-called order of 2.618 is only 2.414. Some mistakes in the derivation leading to such a conclusion are pointed out. Meanwhile, under the assumption that the second derivative of the involved function is bounded, the convergence radius of the secant-like method is given, and error estimates matching its convergence order are also provided by using a generalized Fibonacci sequence.