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gibson:teaching:fall-2016:math753:lu-pivoting

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====== Math 753/853 LU decomposition with pivoting ====== The LU decomposition with pivoting is the factorization of a matrix $A$ into an lower-triangular matrix $L$ and an upper-triangular matrix $U$ with a permutation matrix $P$ applied to $A$ \begin{equation*} PA = LU \end{equation*} The permutation matrix $P$ is crucial to suppressing accumulation of rounding errors in the computation. It's so important that **nobody ever uses LU decomp without pivoting, $A=LU$, in practice.** Here a links to a few good online resources for the LU decomposition * [[https://en.wikipedia.org/wiki/LU_decomposition|Wikipedia]]. Decent general description, an example, and applications to $Ax=b$ and computing $A^{-1}$. * [[http://mathworld.wolfram.com/LUDecomposition.html|Wolfram Alpha]]. Pretty terse description of algorithm and application to $Ax=b$. * [[http://nbviewer.jupyter.org/url/www.maths.usyd.edu.au/u/olver/teaching/MATH3976/notes/12.ipynb|Sheehan Olver's MATH3976 Julia notebook]]. Substantially more detailed example than either of the above.

gibson/teaching/fall-2016/math753/lu-pivoting.1475777862.txt.gz · Last modified: 2016/10/06 11:17 by gibson