Convergence Analysis Of Nonlinear Equations Algorithms

In this paper, we studied the convergences of two deformed Newton iterations and a de-formed Halley iteration. The whole article contains of four chapters. In the first chapter, we used the method of majoring sequences to studied the convergences of Newton's methods of " reducing the counting of derivative" and "without inversing of derivative under weak conditions". In the second chapter, we used the two deformed Newton which was discussed in the chapter 1 to solve the problem of finding the roots of nondifferentiable equations and established convergence theorems using majorant method. In the third chapter, we derive a new family of deformed Halley methods without the evaluation of the second Frechet-derivative to approximate the roots of nondifferentiable equations in Banach space. We also provided a existence-uniqueness theorem and a new system of recurrence relations. In the final chapter, we gived a numerical case based on the third chapter.