Re: Numerical Determinants

*To*: mathgroup at smc.vnet.net*Subject*: [mg13178] Re: Numerical Determinants*From*: Paul Abbott <paul at physics.uwa.edu.au>*Date*: Mon, 13 Jul 1998 07:42:26 -0400*Organization*: University of Western Australia*References*: <6n4o6m$nin@smc.vnet.net> <6n9m67$9hq@smc.vnet.net> <6nnb0k$5em@smc.vnet.net> <6nsj1a$f3t@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Rod Pinna wrote: I tried responding to rpinna at civil.uwa.edu.au but it bounced and you don't seem to be listed on the University of Western Australia CWIS? > Which probably indicates that I should have listened better in first > year mathematics :) > > That was the idea I was following, but since it hadn't been mentioned > as a method in a couple of the texts I consulted, I thought that there > might be something I was missing. Basically, everything talks about > inverting the B matrix, but then doesn't mention what to do in B in > singular. As the above *seemed* obvious, I thought that there might be > a reason it wasn't mentioned. Daniel Lichtblau <danl at wolfram.com> pointed out that numeric stability can be a problem. However, since I recall that your matrices are not large, you can use arbitrary (or fixed) precision to track the stability. Dan also mentioned that by taking the LUDecomposition one can get a good estimate of the matrix condition number, which in turn gives an indication of how good a result might be obtained by using the inverse in this way. If you can guarantee that condition numbers are small for the class of matrix you use then you might even be fine with machine arithmetic. Cheers, Paul ____________________________________________________________________ Paul Abbott Phone: +61-8-9380-2734 Department of Physics Fax: +61-8-9380-1014 The University of Western Australia Nedlands WA 6907 mailto:paul at physics.uwa.edu.au AUSTRALIA http://www.pd.uwa.edu.au/~paul God IS a weakly left-handed dice player ____________________________________________________________________