BRACKETING METHODS

This chapter on roots of equations deals with methods that exploit the. fact that a fuction typically changes sign in the vicinity of a root. These techniques are called bracketing methods because two initial guesses for the root are required. As the name implies, these guesses must "bracket," or be on either side of. the foal.

 The particular methods described herein employ different strategies to systematically reduce the width of the bracket and hence, home in on the correct answer. As a prelude to these techniques, we will briefly discuss graphical methods for depicting functions and their roots.

 Beyond their utility for providing rough guesses, graphical techniques are also useful for visualizing the properties of the functions and the behavior of the various numerical methods.