A Number Of Solutions. Banach Space Convergence Of The Algorithm Of Nonlinear Equations

In recent years, following the development in research of Mathsmatics and the appearence and consummation of mainframe computer, several kinds of non-linear problems have been regarded by many scientists and engineers sooner or later .They have more and more interest in these questions, especially, some key questions in engineering calculation of recent physics and science are depended on the solution of non-linear equation. So the solution of non-linear equation play a important role not only in theoretic research but in application.This paper is made up of three chapter, which discuss mainly about the astringency of the iterative methods and the application in fact. The research of iterative methods becomes hardcore of solution to all kinds of non-linear problems. Whether the non-linear problems will be solved well or not is directed affected by the choice of iterative methods. So it is very important and meaningful to do the research of iterative methods.Chapter one: this chapter discuss mainly about the astringency of several deformed Newton's iterative methods and their application in solution of non-differentiable problems. Newton's method is the heart of classic iteration. Although it is powerful and has fast speed of convergence, its shortcoming is obvious in some realms. In order to solve these shortcoming, several deformed Newton's methods appear. But these methods are designed to solve differen-tiable problems, they will be no use when meeting with non-differentiable equations. Therefor, this chapter puts forward the solution of non-differentiable equations.Chapter two: this chapter discuss mainly about the convergence of Halley's method under more common conditions. Conventional problems of convergence are discussed under Kantorovich condition. The condition which this chapter discusses expand the Kantorovich condition. It will slove more common problems in some degree.Chapter three: this chapter discuss mainly about the convergence of a new hybrid method. If one consigers the fact that the firstderivative of the function may be difficult to compute analytically the new procedure will become an attractive alternative and it has quartic convergence.