On The Convergence Of King-Werner Iteration And Deformed King-Werner Iteration

The algorithm problem of solving the nonlinear operator equationF(x)=0in Banach space has been one of the most interesting problems for many numerical scientists.One of the most efficient algorithms to solve this problem is the iterative method.Whether a nonlinear problem will be solved well or not is directly affected by the choice of iterative method.The King-Werner Method is an efficient one for solving nonlinear equations. The thesis mainly makes analysis on the convergence of King-Werner iter-ative method and the deformed King-Werner iterative method under some weak conditions.This paper consists of three chapters.In Chapter One,we summarize various corrections of Lipschitz condition since Kantorovich condition was put forward,and the convergence theorem of King-Werner method.In Chapter Two,the conditions of some existed convergence theorems are improved.By using the recurrence technique,we obtain the semilocal and local convergence theorems under the condition that the first Fréchet-derivative satisfies Holder condition.The conditions used in this chapter improve the Kantorovich condition,and can be satisfied in more general problems.In Chapter Three,we replace the first derivative in King-Werner method by the first divided difference of F and get the deformed King-Wemer method in Banach spaces.In section two we propose the semilocal and local convergence theorems for the deformed method in Holder condition. In section three,in spirit of Wang Xinghua's work,the semilocal and local convergence theorems are given for the deformed method with the aid of majorizing function under a kind of weaker Lipschitz condition,respec-tively.