Semilocal Convergence Analysis Of A Kind Of Newton-like Method And Inexact Newton Method

To solve the nonlinear equation F(x)=0 is an important project in maths and varies areas. We rarely get the accurate solutions in reality. So the best way to solve the problem is the iterative algorithms. This thesis mainly focus on the semilocal convergence of inexact Newton methods and Newton-like methods. We’ve changed relative conditions to improve some results. The contents are as follows:Chapter 1 introduces the background and relevant preliminary knowledge of tradi-tional iterations, such as iteration of inexact Newton method and Newton-like method, the definition of each kind of convergence, convergence order, condition of continuation and relevant theories. The paper structure is shown at last.In Chapter 2, when solving the equation J(F(x)+G(x))=0, we use A(x) which is the approximate value of F’(x) to take the place of F’(x). Then we present a Newton-like method, and its semilocal convergence under Holder-condition will be obtained according to the character of outer inverse.In Chapter 3, we use the inexact Newton method to explore the approximate solution of F(x)= 0 when F is a Frechet-differentiable operator. By modifying the limiting condition of F and choosing appropriate residual control, we obtain the corresponding semilocal convergence.