Errors during computation:

Truncation Error: true result (input) minus exact arithmetic result from algorithm

i.e. truncating series, replacing derivatives by differences, replacing function by a simpler polynomial, terminating iteration before convergence.

Rounding Error: inexact representation of real numbers and the arithmetic operations upon them.

Usually: Truncation error dominates.

Absolute and Relative Error

Q: What does an error of ``1'' mean?

if counting world population $\Rightarrow$ pretty good (insignificant error)
if counting $\char93$ of people in car $\Rightarrow$ not so good (more significant error)

Abs error = approximate value - true value (could use absolute value)

Rel error = $\frac{\mbox {absolute error}}{\mbox {true value}}$

Not cast in stone: always define what these are.

for real error $\rightarrow$ could use %

However, we seldom know the true value! So we estimate or bound the error.

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