Practice question · Fill in the blanks
Complete the definition of numerical stability.
An algorithm is numerically stable when small errors ______ as the computation proceeds.
Word bank: are removed completely · stay small · grow exponentially · cancel exactly
Hints
- No algorithm can undo a round-off error already committed.
- Stability is about containment, not elimination.
Show the answer
An algorithm is numerically stable when small errors stay small as the computation proceeds.
Why
Stability means errors do not get amplified, they stay small, they are never removed. An unstable algorithm magnifies them, so a computation on essentially exact input can still return a wildly wrong answer.
Practise Numerical Errors and Stability
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