Feb 20 2008

MAIN POINTS
The text defines special arithmetic operations that act within the limits of floating point numbers under the IEEE standard. Tables 1.2 and 1.3 show the difference between using the operations on numbers that are far apart and numbers that are very close. When the two are close, as in Table 1.3, the relative error is much higher. Example 5 stresses how important the formulation of the problem is, because this can affect the number of significant digits. Just formulating the problem as an addition rather that a subtraction can have huge effects on the number of significant digits. The final example uses nesting as a way to minimize error.

CHALLENGES
I'm assuming it's a typo when they say on p.25 that x^3=x^3*x. I feel like it would be challenging to keep track of errors as they propagate through lengthy calculations, if we weren't given an exact value to compare to. It would also be challenging to keep track of all of this while implementing it in software.

REFLECTION
The book truncates numbers to a certain number of base-10 digits. However, isn't this inconsistent with how the numbers are represented within the computer? They would have to be truncated to a certain number of base-2 digits. This probably affects the measure of relative error very slightly.

It's interesting that rounding produces a slightly greater error than truncation in Example 6.