A second-derivative-free modified Secant-like method with order 2.732… for unconstrained optimization

A second-derivative-free modified Secant-like method for solving univariate and unconstrained optimization problems is presented. The new method is proved to have convergence order of 2.732… which is better than the convergence order of 2.414… of the method proposed recently by Kahya [E. Kahya, Modified Secant-type methods for unconstrained optimization. Appl. Math. Comput. 181 (2006) 1349-1356]. Numerical examples are also provided which show that the new method is better than the old one.