A class of exponential quadratically convergent iterative formulae for unconstrained optimization

For solving nonlinear, univariate and unconstrained optimization problems, Newton method is an important and basic method which converges quadratically. This paper presents a class of exponential iterative formulae. Convergence analyses show that the proposed methods converge quadratically. The efficiencies of the methods are analyzed in terms of the most popular and widely used criterion in comparison with the classical Newton method using five test functions. Numerical results indicate that one of the new exponential iterative formulae is effective and comparable to well-known Newton's method.