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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

1 Answer 1

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.

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Thanks, but my question was not how to decompose a matrix into LU. I wanted to know how to use pivoting when doing LU decomposition. –  Tharindu Rusira Nov 26 '11 at 15:58
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@Tharindu: You'll want to see this. –  J. M. Nov 26 '11 at 16:55
    
Got it. thanks all... –  Tharindu Rusira Nov 26 '11 at 17:57

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