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MathGroup Archive 2003

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Re: How to generate Orthogonal Polynomials?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg44397] Re: How to generate Orthogonal Polynomials?
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Sat, 8 Nov 2003 04:50:42 -0500 (EST)
  • Organization: Universitaet Leipzig
  • References: <boftji$5q3$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

<< LinearAlgebra`Orthogonalization`

With[{w = x^2},
  GramSchmidt[{1, x, x^2, x^3}, 
    InnerProduct -> (Integrate[#1*#2*w, {x, -1, 1}] &)
    ]
  ]

Regards
  Jens


Big Oh Rob wrote:
> 
> I'm having problems generating orthagonal polynomials using the
> GramSchmidt function.
> 
> I'm given a weight.
> 
> And my innerproduct looks like:
> 
> <f,g>=Integrate(from -1 to 1)[f(x)g(x)w(x)]
> 
> w(x) is the wight and is give.  It could be anything like x, x^2 or
> x^2+1.
> 
> Any help is appreciated.  Thanks


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