Practice question · Fill in the blanks
Complete the description of partial pivoting.
Partial pivoting swaps rows so that the pivot is ______.
Word bank: the smallest available entry in the column · the largest available entry in the column · always exactly 1 · the first nonzero entry encountered
Hints
- Elimination divides by the pivot, so ask which choice keeps the multipliers small.
- Dividing by a tiny number amplifies whatever error it carries.
Show the answer
Partial pivoting swaps rows so that the pivot is the largest available entry in the column.
Why
Choosing the largest available entry keeps every multiplier at most 1 in size, so round-off is not magnified. Taking the first nonzero entry instead is exactly the self-inflicted instability the lesson warns about.
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