In this first Section concerning numerical methods we will discuss some of the issues involved with doing arithmetic on a computer. This is an important aspect of engineering. Numbers cannot, in general, be represented exactly, they are typically stored to a certain number of significant figures . The associated rounding error and its accumulation are important issues which need to be appreciated if we are to trust computational output.
We will also look at ill-conditioned problems which can have an unfortunate effect on rounding error.
- recall the formula for solving quadratic equations
- round real numbers and know what the associated rounding error is
- understand how rounding error can grow in calculations
- explain what constitutes an ill-conditioned problem
2.1 Rounding error
2.2 Accumulated rounding error
3 Well-conditioned and ill-conditioned problems