CS3414 Afterclass Notes --- 23 May, 2002

1. Introduction

   • Definition of the f(x)=0 problem and several typical characteristics of this problem.

   • Definition of the convergence rate of an iterative algorithm for solving f(x)=0.

2. Methods for solving a single equation f(x)=0.

   We looked at three well-known methods: bisection, newton, secant.

   For each case we gave the idea behind the method, talked about assumptions each make, convergence rate for each, and a little about what can go wrong. Most of this follows the text very closely.

   Also mentioned that there are fancier methods (e.g., based on using more than two pieces of information to generate the new guess) and also hybrid schemes (e.g., slow-and-safe initially, switching to faster method as convergence nears).