Convergence Analysis Of Newton Method Under Two Types Of Weak H(?)lder Conditions

The solving problem of nonlinear operator equations as a hot topic in the field of numerical analysis,not only occupies an important position in pure mathematics and applied mathema.tics,but also has a wide range of practical applications in engineering,physical,economic,financial and other fields.To solve the nonlinear equations,people usually create a convergent sequence to approximate the solution of an equation by some iterative methods.In this thesis,we mainly concerns the local convergence and semi-local convergence of Newton method for solving a nonlinear operator equation F(x)= 0.The contents are as follows:In Chapter 1,we introduce the development of iterations for solving nonlinear opera-tor equations,especially the application of the radius Lipschitz condition with L average and the technique of recurrence sequence in the study of iterative methods,including the convergence conditions,the convergence order,the radius of convergence ball and the uniqueness ball for the solutions of equations and the basic concepts and related knowledge of this thesis.Finally,the main results of this paper are given.In Chapter 2,under the affine radius H(?)lder condition with L average for F',the local convergence of classical Newton method for solving nonlinear equations was studied.Some local convergence conditions were given.The R-order of convergence was proved to be at least 1+p under those conditions,and some corollaries were presented.In Chapter 3,under H(?)lder condition with L average for F',by the technique basedon recurrence relations instead of majorant principle,the semi-local convergence theorem was obtained.And we enlarge the range of the convergence domain and improve the priori error estimates of the iterative method.