For Solving Nonlinear Equations Of Convergence Of The Algorithm Analysis

When we use mathematical methods to study natural phenomena and practical problems , or solve engineering technique problems , we often regard these practical problems as the algorithm problems of solving nonlinear equations in Banach space. This important problem has been the core of studies of numerical workers, and the iteration algorithm is the most important method of solving the nonlinear equations. 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.As we are all known, first, the well-known iteration is no other than Newton's iteration, it has second-order convergence, Second, there are third-order Chebyshev's iteration, Halley's iteration, Super-Halley's iteration and their deformations. Besides, there is fourth-order Jarratt's iteration and so on.The dissertation contains four chapters, mainly makes analyses on the deformations of Newton's method and convergence of a family of iterations with cubic order which can avoid the computation of the second Frechet-derivative.In chapter 1, we discuss several iterative methods and their convergence conditions. While, we also present the techniques in proving the convergence theorem.In chapter 2, we study the improvement of a modified Newton method for polynomials and analyse its convergence.In chapter 3, we derive the second -order-derivative-free iterations with two parameters from the third-order iterations with one parameter to approximate the roots of nondifferentiable equations in Banach space, and we also give and prove the convergence theorem.In chapter 4, we give some numerical examples.