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}}