A Newton-like iterative method for solving nonlinear equations

In this paper,a class of Newton-like iterative method by combining Newton-Raphson method and secant method is proposed to solve non-linear equations.The nested interval theorem is used to prove the convergence of this kind of numerical calculation and a method of giving after-event error assessment is also presented.Numerical experiments indicate that,on condition that the concave-convex hypothesis in this paper is satisfied,this new method has better convergence rate than both Newton method and secant iteration,especially in the case of solving the single root of nonlinear equation in large interval.