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LU decomposition: Difference between revisions
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correction: there stood "columns" where rows was meant
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We see in the second formula that to get the <math>l_{ij}</math> below the diagonal, we have to divide by the diagonal element (pivot) <math>u_{jj}</math>, so we get problems when <math>u_{jj}</math> is either 0 or very small, which leads to numerical instability.
The solution to this problem is ''pivoting'' <math>A</math>, which means rearranging the rows of <math>A</math>, prior to the <math>LU</math> decomposition, in a way that the largest element of each column gets onto the diagonal of <math>A</math>. Rearranging the
:<math>PA \Rightarrow A'</math>
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