Practice question · Put in order
Order the steps of curing a formula that loses accuracy to cancellation.
- Identify where two nearly equal quantities are subtracted
- Rewrite the expression algebraically to remove that subtraction
- Adopt the form whose error stays small
- Compare both forms on a case where the cancellation bites
- Check that the rewritten form is mathematically equivalent
Hints
- You cannot rewrite what you have not located.
- Equivalence must be verified before accuracy is even worth testing.
Show the answer
- Identify where two nearly equal quantities are subtracted
- Rewrite the expression algebraically to remove that subtraction
- Check that the rewritten form is mathematically equivalent
- Compare both forms on a case where the cancellation bites
- Adopt the form whose error stays small
Why
Locate, rewrite, verify equivalence, test on a hard case, adopt. Skipping the equivalence check is how a 'more stable' formula quietly becomes a formula for a different quantity.
Practise Numerical Errors and Stability
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