Practice question · Sort into groups
Sort each source of error by its kind.
Groups: Round-off error · Truncation error
- Stopping a Taylor series after four terms
- Using 100 rectangles in place of a limit
- The last bits lost when two floats are added
- Approximating a derivative by a difference quotient with h = 0.01
- Storing one third as a finite binary fraction
Hints
- Truncation error would remain even on a machine with infinite precision.
- Round-off error would remain even if the method were exact.
Show the answer
Round-off error: Storing one third as a finite binary fraction, The last bits lost when two floats are added
Truncation error: Stopping a Taylor series after four terms, Using 100 rectangles in place of a limit, Approximating a derivative by a difference quotient with h = 0.01
Why
Truncation error is the error of the METHOD, stopping an infinite process early, and is independent of the machine. Round-off is the error of the REPRESENTATION and would persist under a perfect method. Separating the two is what lets you attack each.
Practise Numerical Errors and Stability
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