Modified Secant-type methods for unconstrained optimization

For solving nonlinear, univariate and unconstrained optimization problems, Newton method is an important and basic method which convergences quadratically. In this paper, we suggest a family of three new modifications of the classical Secant method where the iteration formula including an approximation of f″(xk) is satisfied by a recursive scheme. The efficiencies of the new methods are analyzed in terms of the most popular and widely used criterion; the number of iterations, in comparison with the Newton and Secant methods using six test functions.