Implementing Newton's Method

Abstract

Newton's Method, the recursive algorithm for computing the roots of an equation, is one of the most efficient and best known numerical techniques. The basics of the method are taught in any first-year calculus course. However, in most cases the two most important questions are often left unanswered. These questions are, "Where do I start?" and "When do I stop?" We give criteria for determining when a given value is a good starting value and how many iterations it will take to ensure that we have reached an approximate solution to within any predetermined accuracy.