Accelerated iterative method for finding zeros of nonlinear functions

Abstract

Keywords: Halley's method, Gamma distribution, Newton's method, Schwarzian Newton method. The dissertation in three chapters presents interesting results on convergence of Newton's method, Halley's method and Schwarzian Newton's method and their applications to nd the inversion of gamma distribution. This dissertation also presents an interesting numerical simulation result by comparing the iterative methods Newton's method, Schwarzian Newton's method and Average Newton's method. Chapter 1 provides basic results towards the convergence of Newton's method and the development of various modi cation of Newton's method. Chapter 2 presents the Schwarzian Newton's method and its nonlocal convergence property and its application to nd the inversion of gamma distribution. This chapter is based on the recent work of J. Segura. Chapter 3 presents the numerical simulation results by comparing various Newton's methods. In this section, the Schwarzian Newton's method is applied to the normal distribution and generalize gamma distribution.