# LU Decomposition

Can we use partial pivoting when obtaining the upper triangular matrix using Gaussian elimination? If so, how can we do it?

Let $Ax=B$ and $A=LU$

To determine $L$, it seems fancy to use pivoting as we interchange rows in $A$, since we are using the factors used in Gaussian elimination which were found during the search for $U$.

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"Urgent" is not a good word to use here when asking us questions. We are not your horses to be whipped. – J. M. Nov 26 '11 at 14:03
In any event: yes, you can do Gaussian elimination with partial pivoting. The decomposition goes like $\mathbf P\mathbf A=\mathbf L\mathbf U$, where $\mathbf P$ is a permutation matrix. – J. M. Nov 26 '11 at 14:05

If you have $A=L U$ then solving $Ax = b$ is equivalent to solving first $L y = B$ and then $U x=y$. The point being, both of those can be done very easily since they are triangular systems.