[SciPy-User] orthogonal polynomials ?

[josef.pktd at gmail.com]

On Sat, May 14, 2011 at 4:25 PM, Christopher Jordan-Squire
<cjordan1 at uw.edu> wrote:
> I think what you're looking for are the Legendre polynomials. They're
> orthogonal on [-1,1] with respect to the uniform weights, while Hermite
> polynomials are orthogonal with respect to a gaussian weight.
> Be careful, though. The legendre polynomials in scipy.special are orthogonal
> but they aren't normalized.
> -Chris

Thanks, I missed that.

To continue with Nicky's link:
http://en.wikipedia.org/wiki/Legendre_polynomials  including graphs
http://en.wikipedia.org/wiki/Legendre_polynomials#The_orthogonality_property

normalization might not matter for what I'm planning to do, but I will check.

Josef

>
>
> On Sat, May 14, 2011 at 1:11 PM, 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
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