The Analysis Of Some High-Order Iteratives For Solving Nonlinear Equations

In this thesis, we mainly study the basic algorithm problem of solving nonlinear operator equation F(x)=0 in Euclidean spaces. Such problem has been studied by many mathematicians and engineers. One of the most important methods to solve this kind of equation is iterative method. So it is very important and meaningful to do the research of iterative methods.In the first chapter, by analyzing and summarizing the achievements of domestic and foreign researchers in this domain, the article expounds the significance and practi-cal background of solving nonlinear equations by iterative methods. At the same time, we give some basic definitions and notations which will be used throughout the whole thesis.In the second chapter, we study the convergence of Newton-Jarratt method under the weak gamma condition, which is from the weak Smale' point estimate condition. The proofs of the existence and convergence theorems are given.In the third chapter, under the radius Lipschitz condition with the L-average, we discuss the convergence property of a third order modified Chebyshev method, The advantage of this condition is that it unifies the weak Smale'point estimate condition and Kantorovich-type condition.In the fourth chapter, we present a united structural approach for a special type of high-order iterative methods which not only can avoid the computation of the second Frechet-derivative but also has the convergence of cubic order. Several numerical ex-amples are given to illustrate the performance of the presented methods by comparing with some other methods.