Review Questions for Rounding

1. Given a real number, what is the rounding error involved in storing it as a machine number? What is the relative error?
2. How can we bound the relative error of representing a real number as a normalized machine number?
3. What is cancellation? Why is it a problem?
4. What types of operations lead to catostrophic cancellation?
5. Given two different equations for evaluating the same value, can you identify which is more accurate for certain x and why?