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[math] Chebyshev polynomial

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[math] Chebyshev polynomial

Boost - Dev mailing list
Does Boost.Math contain functions for Chebyshev polynomials? Preferably
a recurrent chebyshev_next().

I can find functions for Legendre, Laguerre, and Hermite polynomials,
but not Chebyshev.


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Re: [math] Chebyshev polynomial

Boost - Dev mailing list

> On 13 May 2017, at 10:35, Bjorn Reese via Boost <[hidden email]> wrote:
>
> Does Boost.Math contain functions for Chebyshev polynomials? Preferably
> a recurrent chebyshev_next().
>
> I can find functions for Legendre, Laguerre, and Hermite polynomials,
> but not Chebyshev.

I second that request. Chebyshev polynomials are extremely useful in numerical applications:

- evaluation does not loose precision even if the polynomial order is huge (order 1000 is no problem)
- coefficients can be computed in O(N log(N)) with a FFT

Best regards,
Hans

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Re: [math] Chebyshev polynomial

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In reply to this post by Boost - Dev mailing list


On 13/05/2017 09:35, Bjorn Reese via Boost wrote:
> Does Boost.Math contain functions for Chebyshev polynomials? Preferably
> a recurrent chebyshev_next().

No it doesn't as yet.

However, the recurrence relation is trivial, likewise evaluation of an
arbitrary Tn(x) in terms of trig functions?  Even the roots have simple
formulae.

What did you want to do?

John.

>
> I can find functions for Legendre, Laguerre, and Hermite polynomials,
> but not Chebyshev.
>
>
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Re: [math] Chebyshev polynomial

Boost - Dev mailing list
In reply to this post by Boost - Dev mailing list
On 05/15/2017 02:29 PM, John Maddock via Boost wrote:

> However, the recurrence relation is trivial, likewise evaluation of an
> arbitrary Tn(x) in terms of trig functions?  Even the roots have simple
> formulae.

They are indeed trivial, and I already have my own implementation.

I just thought it might be nice to have in Boost.Math as we already
have support for other polynomials.

> What did you want to do?

I am using it for function approximation:

 
https://en.wikipedia.org/wiki/Approximation_theory#Chebyshev_approximation

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