Iterative Methods for Nonlinear Systems

Abstract

In this chapter we will study the solution of systems of nonlinear equations. As opposed to linear equations, no explicit solution techniques are, in general, available for nonlinear equations, and hence their solution completely relies on iterative methods. In the first section we shall begin with the application of the Banach fixed point theorem for systems of nonlinear equations with one or several variables. Given the fact that iterative techniques have a long history in mathematics, the significance of Banach’s fixed point theorem originates from its unified approach, covering a wide variety of different successive approximation methods.