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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

• Follow-Ups:
  • Re: LU Decomposition w/o Pivoting
    • From: danl@wolfram.com