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