MULTIPOINT METHODS FOR SOLVING NONLINEAR EQUATIONS

Chapter 1

Basic concepts

In this book we are mainly concerned with multipoint methods for solving nonlinear equations, a special class of iterative methods that possess a greater computational efficiency than classical one-point methods. To develop multipoint methods and investigate their convergence characteristics and computational efficiency, in this chapter we give some basic concepts and properties of root-solvers. Following Traub’s approach (Traub, 1964), we first expose a natural classification of iterative methods relied on the required information from the current and previous iterations. Properties of iterative root-finding methods of paramount importance, such as order of convergence, computational efficiency, the choice of initial ...