### Introduction

There are occasions when direct methods (like Gaussian elimination or the use of an $LU$ decomposition) are not the best way to solve a system of equations. An alternative approach is to use an iterative method. In this Section we will discuss some of the issues involved with iterative methods.

#### Prerequisites

• revise matrices, especially the material in HELM booklet 8
• revise determinants
• revise matrix norms

#### Learning Outcomes

• approximate the solutions of simple systems of equations by iterative methods
• assess convergence properties of iterative methods