# Big Theta Complexity of Gaussian Elimination using Complete Pivoting

I already know the Big O for partial pivoting is $$O(n^3)$$ and remain the same for complete pivoting. I also know the big theta complexity for partial pivoting is $$2/3 n^3$$

I would like to know the complexity of complete pivoting in big theta

From the $$\frac23n^3$$ number you are reporting, I presume you are counting either multiplications or FMAs as your basic operations, which is one of the possible way to count "flops", or floating point operations.
In this case, the pivoting requires zero floating point operations, so it costs zero. The cost of GECP is still $$\frac23n^3$$. It is a weakness of the flops model that it cannot tell the two apart.