Some sources say it is $O(n^3)$, others that it is $n^3/3+O(n^2)$ and on the stackexchange it is $2/3n^3$. I am not very good with the big O notation, can someone explain which answer is the most precise?
2026-02-24 11:56:20.1771934180
What is the complexity of the LU factorization?
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Matrix operations tend to cast most computation in terms of a Fused Multiply-Add (FMA). Some consider this to count as one floating point operation. Others count the multiply and add separately.
If you count FMAs, then the cost of an LU factorization is approximately $1/3 n^3$. If you count multiplies and adds separately, then the cost is $1/3 n^3$ multiplies and $1/3 n^3$ adds, and hence you end up with $2/3 n^3$ floating point operations (flops).
If Wikipedia says the count is the same as matrix multiplication, then Wikipedia is wrong.