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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