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Cholesky Decomposition

  • To: mathgroup at smc.vnet.net
  • Subject: [mg104516] Cholesky Decomposition
  • From: Lars Schouw <schouwla at yahoo.com>
  • Date: Tue, 3 Nov 2009 02:51:39 -0500 (EST)

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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