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