Introduction to Numerical Analysis and Scientific Computing

Chapter 2

Finding Roots of Real Single-Valued Functions

2.1Introduction

2.2How to Locate the Roots of a Function

2.3The Bisection Method

2.4Newton’s Method

2.5The Secant Method

2.6Exercises

2.7Computer Projects

In this chapter we consider one of the most encountered problems in scientific computing, which is the problem of computing the root or zero of a realvalued function f of one variable. We focus on what we consider to be three basic methods: the bisection, Newton’s and the secant methods. In short, any of these methods compute a solution of a nonlinear equation starting from one initial data, then adopting some iterative method that- under favorable conditions- will converge to a zero of the function f.

To study other methods, we refer ...