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Re: Inversion using Cholesky Decomposition

• To: mathgroup at smc.vnet.net
• Subject: [mg46608] Re: Inversion using Cholesky Decomposition
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Wed, 25 Feb 2004 13:07:02 -0500 (EST)
• Organization: Universitaet Leipzig
• References: <c1h0kf$9ra$1@smc.vnet.net>
• Reply-to: kuska at informatik.uni-leipzig.de
• Sender: owner-wri-mathgroup at wolfram.com

Hi,

this is a bug in the documentation, Inverse[] accept
only the Method options for exact matrices, i.e. ,
CofactorExpansion, DivisionFreeRowReduction and OneStepRowReduction.

But you can use CholeskyDecomposition[] and compute 
the inverse by yourself

Regards
  Jens

Johannes Ludsteck wrote:
> 
> 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