Talk:Gaussian elimination: Difference between revisions
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What is the relationship of this task to [[LU decomposition]]? –[[User:Dkf|Donal Fellows]] 09:01, 12 February 2012 (UTC)
:Basically, Gaussian elimination is the same as LU decomposition followed by backsubstitution. To solve the system AX=B with LU decomposition, you multiply on the left by P: PAX=PB, hence LUX=PB. Then you solve first the lower triangular system LZ=PB, which gives a vector Z (or matrix if B is a matrix, which happens if you want to solve several systems at the same time with the same matrix A). Then you solve the upper triangular system UX=Z, and you are done.
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