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