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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