[SciPy-User] orthogonal polynomials ?

[Lou Pecora]

The [0,1] requirement still allows use of the Legendre polynomials.  Just use 
L_n(2y-1) for y in [0,1].  The weight stays uniform but changes by a factor of 2 
(that can be absorbed in the normalization coefficient if you want.
 -- Lou Pecora,   my views are my own.



----- Original Message ----
From: nicky van foreest <vanforeest at gmail.com>
To: SciPy Users List <scipy-user at scipy.org>
Sent: Sat, May 14, 2011 3:27:07 PM
Subject: Re: [SciPy-User] orthogonal polynomials ?

Ah, I missed your extra requirement that the weight function should be
uniform.... and on the interval [0,1]. I suspect you searched on
google, The Legendre have uniform weight, but live on [-1,1].


On 14 May 2011 22:11, nicky van foreest <vanforeest at gmail.com> wrote:
> Hi,
>
> Might this be what you want:
>
> The first eleven probabilists' Hermite polynomials are:
>
> ...
>
> My chromium browser does not seem to paste pngs. Anyway, check
>
>
> http://en.wikipedia.org/wiki/Hermite_polynomials
>
> and you'll see that the first polynomial is 1, the second x, and so
> forth. From my courses on quantum mechanics I recall that these
> polynomials are, with respect to some weight function, orthogonal.
>
> Nicky
>
>
>
> On 14 May 2011 22:02,  <josef.pktd at gmail.com> wrote:
>> Suppose I have an polynomial basis on a bounded domain [0,1] , the
>> polynomials in scipy are orthogonal with respect to a weighting
>> function, for example Chebychev.
>>
>> What I would like:
>> First component is constant
>> second component is linear trend
>> all other components are orthogonal to all previous ones with respect
>> to uniform weights.
>>
>> Is there a ready way how to do this? (Or it's easy and I can figure it
>> out myself?)
>> Or does what I would like not make any sense?
>>
>> Josef
>> _______________________________________________
>> SciPy-User mailing list
>> SciPy-User at scipy.org
>> http://mail.scipy.org/mailman/listinfo/scipy-user
>>
>
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