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MathGroup Archive 2005

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Re: GramSchmidt problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg57035] Re: GramSchmidt problem
  • From: David Bailey <dave at Remove_Thisdbailey.co.uk>
  • Date: Thu, 12 May 2005 22:44:18 -0400 (EDT)
  • References: <d5uvda$9at$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Heath Gerhardt 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:
> 
> \!\({1\/2\ \((3 + \@5)\), 1\/2\ \((\(-3\) - \@5)\), 1\/2\ \((1 + \@5)\), 0, 
>     1\/2\ \((\(-1\) - \@5)\), 1\/2\ \((\(-3\) - \@5)\), 1\/2\ \((3 + \@5)\), 
>     1\/2\ \((\(-1\) - \@5)\), 0, 1\/2\ \((1 + \@5)\), 1\/2\ \((1 + \@5)\), 
>     1\/2\ \((\(-1\) - \@5)\), 1, 0, \(-1\), 0, 0, 0, 0, 0, 
>     1\/2\ \((\(-1\) - \@5)\), 1\/2\ \((1 + \@5)\), \(-1\), 0, 1}\)
> 
> \!\({1\/2\ \((1 + \@5)\), 1\/2\ \((\(-3\) - \@5)\), 1\/2\ \((3 + \@5)\), 
>     1\/2\ \((\(-1\) - \@5)\), 0, 1\/2\ \((\(-1\) - \@5)\), 
>     1\/2\ \((3 + \@5)\), 1\/2\ \((\(-3\) - \@5)\), 1\/2\ \((1 + \@5)\), 0,
> 1, 
>     1\/2\ \((\(-1\) - \@5)\), 1\/2\ \((1 + \@5)\), \(-1\), 0, 0, 0, 0, 0, 
>     0, \(-1\), 1\/2\ \((1 + \@5)\), 1\/2\ \((\(-1\) - \@5)\), 1, 0}\)
> 
> \!\({1\/2\ \((1 + \@5)\), 1\/2\ \((\(-1\) - \@5)\), 1, 0, \(-1\), 
>     1\/2\ \((\(-3\) - \@5)\), 1\/2\ \((3 + \@5)\), 1\/2\ \((\(-1\) - \@5)\), 
>     0, 1\/2\ \((1 + \@5)\), 1\/2\ \((3 + \@5)\), 1\/2\ \((\(-3\) - \@5)\), 
>     1\/2\ \((1 + \@5)\), 0, 1\/2\ \((\(-1\) - \@5)\), 
>     1\/2\ \((\(-1\) - \@5)\), 1\/2\ \((1 + \@5)\), \(-1\), 0, 1, 0, 0, 0, 0, 
>     0}\)
> 
> \!\({1, 1\/2\ \((\(-1\) - \@5)\), 1\/2\ \((1 + \@5)\), \(-1\), 0, 
>     1\/2\ \((\(-1\) - \@5)\), 1\/2\ \((3 + \@5)\), 1\/2\ \((\(-3\) - \@5)\), 
>     1\/2\ \((1 + \@5)\), 0, 1\/2\ \((1 + \@5)\), 1\/2\ \((\(-3\) - \@5)\), 
>     1\/2\ \((3 + \@5)\), 1\/2\ \((\(-1\) - \@5)\), 0, \(-1\), 
>     1\/2\ \((1 + \@5)\), 1\/2\ \((\(-1\) - \@5)\), 1, 0, 0, 0, 0, 0, 0}\)
> 
> 
> thanks in advance
> Heath
> 
Like many Mathematica operations, GramSchmidt can operate with exact 
quantities (Integers, Fractions, Roots, etc.) yielding an exact result, 
or with real numbers yielding a real (inexact) result. All Your numbers 
are exact, so it will try to give you an exact answer. Unfortunately, 
the size of the numerators/denominators of the terms will explode. Just 
apply N to your vectors before you start, and you will obtain an answer 
easily.

BTW, please use InputForm when submitting examples - reading box form is 
a bit like reading punched paper tape!

David Bailey
http://www.dbaileyconsultancy.co.uk


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