ABSTRACT
This chapter discusses a framework to study fixed point problems, through the use of what is called function iteration. Analysis, with its emphasis on understanding sequence and function convergence rates, is a necessary tool for analyzing numerical approximation techniques. The chapter focuses on Newton’s Method, which is a classic numerical method for approximating a root of a function. When solving problems in the real world, we often forego finding an exact solution and instead try to find approximate solutions using a variety of techniques which we generally call numerical approximation. The chapter outlines the basic theory and explores how the theory is really a close relative of the fixed point process.
