There are occasions when direct methods (like Gaussian elimination or the use of an 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.
- revise matrices, especially the material in HELM booklet 8
- revise determinants
- revise matrix norms
- approximate the solutions of simple systems of equations by iterative methods
- assess convergence properties of iterative methods
1.1 The Jacobi iteration
1.2 Gauss-Seidel iteration
2 Do these iterative methods always work?
2.1 Guaranteed convergence
2.2 What’s so special about strict diagonal dominance?
3 Engineering Example 1
3.1 Detecting a train on a track