On the set of initial guesses for the secant method

The secant method is the most used iterative to solve an operator equation where involved nondifferentiable. A known problem that arises when applying this its accessibility. Then, we try improve it by using technique of decomposition involved, so in turn sum two operators, one differentiable and other continuous but not differentiable. For this, use a family Newton-secant-type methods from Newton's well-known secant-type methods. We study accessibility new different ways: From convergence balls methods, obtained local convergence, dynamic Some examples related chemistry are also presented prove theoretical results.