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Re: Cholesky Decomposition

  • To: mathgroup at smc.vnet.net
  • Subject: [mg104565] Re: Cholesky Decomposition
  • From: dh <dh at metrohm.com>
  • Date: Wed, 4 Nov 2009 01:33:36 -0500 (EST)
  • References: <hconfo$11e$1@smc.vnet.net>


Hi Lars,

LU and Cholesky are two different compositions of a matrix. 

LUDecomposition does not give the "square root" of a matrix like 

CholeskyDecomposition does. Look it up in the manual.

Daniel



Lars Schouw wrote:

> How do I get out the lower triangular matrix after doing a Choleseky

> decomposition?

> 

> I tried a LU decomposition but not get back what I expect.

> 

> For example the symetrix matrix A

> 1 1 1 1

> 1 5 5 5

> 1 5 14 14

> 1 5 14 15

> 

> is equal to the product of the tringular matrix L and its transposed

> L^T

> 1 1 1 1                    1 0 0 0      1 1 1 1

> 1 5 5 5         =         1 2 0 0      0 2 2 2

> 1 5 14 14                 1 2 3 0      0 0 3 3

> 1 5 14 15                 1 2 3 1      0 0 0 1

> 

> With L

> 1 0 0 0

> 1 2 0 0

> 1 2 3 0

> 1 2 3 1

> 

> But in Mathematica I do this:

> A = {{1, 1, 1, 1}, {1, 5, 5, 5}, {1, 5, 14, 14}, {1, 5, 14, 15}}

> {lu, p, c} = LUDecomposition[A]

> l = lu SparseArray[{i_, j_} /; j < i -> 1, {4, 4}] + IdentityMatrix[4]

> 

> and get

> {{1, 0, 0, 0}, {1, 1, 0, 0}, {1, 1, 1, 0}, {1, 1, 1, 1}}

> 

> Any idea what I am doing wrong?

> 

> Lars

> 

> 




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