Re: Cholesky Decomposition

• To: mathgroup at smc.vnet.net
• Subject: [mg104599] Re: Cholesky Decomposition
• From: Bill Rowe <readnews at sbcglobal.net>
• Date: Wed, 4 Nov 2009 01:40:12 -0500 (EST)

```On 11/3/09 at 2:51 AM, schouwla at yahoo.com (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

What you describe here is a Cholesky decomposition which is
consistent with the subject of your post. So, why are you
working with a LU decomposition? Mathematica will do Cholesky
decompositions. That is

In[15]:= m = {{1, 1, 1, 1}, {1, 5, 5, 5}, {1, 5, 14, 14}, {1, 5, 14,
15}};
CholeskyDecomposition[m]

Out[16]= {{1, 1, 1, 1}, {0, 2, 2, 2}, {0, 0, 3, 3}, {0, 0, 0, 1}}

```

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