A Fast Algorithm Of Solving Nonlinear Equation

Firstly in this paper we give some basic definitions summarize several famous iterative methods and the techniques in proving the iterative methods' convergence theorem. Apply to the thought of two-step, we gained a fast algorithm of solving nonlinear equation through improving the Newton's method. In allusion to Halley's method, we gained a special type of high-order iterative methods that two-step Halley's method applied to Halley-method's geometry in character. Finally we give the numerical results with a number of function tests to show that the new method works better in efficiency compared with the classical methods from Newton's method, Halley's method and two-step Halley's method.