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MathGroup Archive 2005

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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

-- 
Paul Abbott                                      Phone: +61 8 6488 2734
School of Physics, M013                            Fax: +61 8 6488 1014
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AUSTRALIA                               http://physics.uwa.edu.au/~paul
        http://InternationalMathematicaSymposium.org/IMS2005/


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