Re: GramSchmidt problem
- To: mathgroup at smc.vnet.net
- Subject: [mg57044] Re: GramSchmidt problem
- From: Paul Abbott <paul at physics.uwa.edu.au>
- Date: Thu, 12 May 2005 22:44:28 -0400 (EDT)
- Organization: The University of Western Australia
- References: <d5uvda$9at$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
In article <d5uvda$9at$1 at smc.vnet.net>,
Heath Gerhardt <heathgerhardt at hotmail.com> wrote:
> Does anyone know if there are any know problems with GramSchmidt
> crashing Mathematica? When I run it on these 4 25-dimensional vectors it
> crashes on my system:
Tt works perfectly with floating point vectors so I expect that it
crashes because it is not simplifying the intermediate radical
expressions.
Here is functional code for computing GramSchmidt:
GramSchmidt := Fold[Append[#1, FullSimplify[
(#/Norm[#]&)[Fold[Projection, #2, #1]]]] & , {}, #1] & ;
where the projection operator is
Projection[f_, g_] := FullSimplify[f - (f.g) g]
FullSimplify has been used in both routines so that expressions
involving radicals are completely simplified.
Calling your set of 4 vectors mat, one computes the orthonormal vectors
using
GramSchmidt[mat]
As a check,
Simplify[% . Transpose[%]]
Cheers,
Paul
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Paul Abbott Phone: +61 8 6488 2734
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