With Regard To The Convergence Analysis Of A Number Of Iterative Algorithm

The algorithm problem of solving nonlinear operator equationF(x) = 0in Banach space has been studieded by many numerical scientists. The iterative method is a main algorithm for solving nonlinear equation.Now, the research of iterative methods becomes the hardcore of the solution to all kinds of nonlinear problems. Whether the nonlinear problems will be solved well or not is directly affected by the choice of iterative methods. So it is very important and meaningful to do the research of iterative methods.This paper consists of five chapters, which discuss mainly about the convergence of several iterative methods. In Chapter 1, we summarize several iterative methods and their convergence condition, the techniques in proving the iterative methods's convergence theorem.In Chapter 2, we present a family of iterative method with the convergence of order three. The family of iterative methods avoid evaluating the second Frechet derivative. In this Chapter, we establish convergence theorem by using the majorizing method.In Chapter 3,the correction of Super-Halley iterative method is presented. The Super-Halley iterative method has the three-order convergence, but the correction has the four-order. In this Chapter, we establish convergence theorem by using the recurrence relations.In Chapter 4, the convergence of the Newton-like iterative method is given under the new condition.In Chapter 5, the dynamics for the iterative methods in Chapters 2 and 4 is analyzed.Finally ,we give two numerical examples.