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LU Decomposition w/o Pivoting
- To: mathgroup at smc.vnet.net
- Subject: [mg91711] LU Decomposition w/o Pivoting
- From: Benjamin Reedlunn <breedlun at umich.edu>
- Date: Sat, 6 Sep 2008 02:07:07 -0400 (EDT)
Hello,
I am trying to calculate the signs of the eigenvalues of a bunch of
moderately large matrices (thousand by thousand), which takes a long
time. It has come to my attention that the diagonal terms in a LU
decomposition have the same signs as the eigenvalues. So I'm hoping
that the LU decomposition is faster than calculating the actual
eigenvalues. I tried testing this out using mathematica's built in
function LUDecomposition[] and after a large amount of monkeying
around, I realized the signs of the diagonal terms only match the
eigenvalues if there is no pivoting employed. Unfortunately, I cannot
figure out how to turn off pivoting in LUDecomposition[]. While I am
sure I could write my own LU decomposition function, I'm also sure it
would not be nearly as elegant and computationally efficient as the
built in function. So does anyone know how to turn off
LUDecomposition[] or have optimized code to perform a LU decomposition?
-Ben Reedlunn
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