Numerical Methods For Solving Nonlinear Equations At Singularpoint

In this paper,some iterate methods for solving singular problem are studied. The main results are as following 1. As the calculation of Chord methods is cheap and it is easy to use it, Chord methods are always attentioned. In the paper,a class of Chord methods are discussed. Under the conditions that the dimensions of the null space are one or finite,the convergence of Chord methods is proved,the error estimation is obtained and the numerical example is also given. 2. The extrapolation methods have many applications in series calculations, circumference rate calculations,difference scheme and finite methods. In this paper,the extrapolation techniques are used to construct new iterate schemes, that can faster the convergence rate of the scheme. 3. Halley methods,Chebyshev methods and Supper-Halley methods are widely used to find the solution of the equation F ( x)=0. In the paper, the methods above are studied for element solve singular problems the convergence of the method is proved and the error estimate is also obtained. 4. The new iterate schemes are constructed for solving singular problems by using the geometry properties in Hilbert space,the rate of convergence of the methods is also obtained.