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Inversion using Cholesky Decomposition

• To: mathgroup at smc.vnet.net
• Subject: [mg46587] Inversion using Cholesky Decomposition
• From: "Johannes Ludsteck" <johannes.ludsteck at wiwi.uni-regensburg.de>
• Date: Tue, 24 Feb 2004 21:04:41 -0500 (EST)
• Organization: Universitaet Regensburg
• Sender: owner-wri-mathgroup at wolfram.com

Dear MathGroup Members, 
I have to invert large (sparse) positive definite 
symmetric  matrices. The fastest way to perform 
these inversions would  be to use the Cholesky 
decomposition. I read in the  documentation for 
Inverse: 

"A Method option can also be given. Possible     
settings  are as for LinearSolve." 

However, when I tried to give the option 
Inverse[m, Method->Cholesky], 
Mathematica answers with an error message. 

It is, of course, possible to perform the inversion 
by hand,  i.e. to obtain the CholeskyDecomposition[] 
of the matrix and  to compute the inverse by forward 
or backward substitution.  This is, however, slower 
than calling Inverse directly  because the 
substitution does not allow to exploit the  highly 
efficient internal Mathematica code. 

Two Questions: 
[1] Is there any way to provide the Cholesky option 
to  Mathematica? 

[2] Or checks Mathematica automatically whether the 
cholesky  decomposition is applicable?   

Thanks for help, 
	Johannes Ludsteck
<><><><><><><><><><><><><><><><><><>
Johannes Ludsteck
Institut fuer Volkswirtschaftslehre
Lehrstuhl Prof. Dr. Moeller
Universitaet Regensburg
Universitaetsstrasse 31
93053 Regensburg
Tel +49/0941/943-2741