
Boost Users : 
From: Nick Thompson (nathompson7_at_[hidden])
Date: 20200222 14:07:39
I get the feeling that you want to compute the coefficients of the polynomial in the standard basis:
c0 + c1*x + ...
Unfortunately, this is a bad idea, because the computation is horrifically illconditioned. That's why the boost version expands the LegendreStieltjes polynomials in the Legendre polynomial basisthis is wellconditioned. I vaguely recall that expansion in the Chebyshev basis is also wellconditioned, but we succeeded in the Legendre basis and were happy.
The code, to my eyes, is legible, with references to papers and equations within papers:
What are you trying to accomplish by computing these polynomials? The only application I know of is GaussKronrod quadrature, so I'd be interested if you have another application . . .
â€â€â€â€â€â€â€ Original Message â€â€â€â€â€â€â€
On Friday, February 21, 2020 10:25 PM, N A <testrope_at_[hidden]> wrote:
> Hi
>
> The Legendre polynomials (Lp) of degree n=5 and x=0.2 is 0.30752 and according to Boost article, the LegendreStieltjes polynomials (LSp) of degree n=5 and x=0.2 is 0.53239.
>
> So if I want to compute the LSp for n=6, how do I do it? What is the formula you are using to be able to calculate the LSp for any nth degree?
>
> If a recurrence relation is not possible, then is there a closed form mathematical representation to calculate any nth degree LSp?
>
> Thanks
>
> On Friday, February 21, 2020, 06:54:27 PM GMT+4, Nick Thompson via Boostusers <boostusers_at_[hidden]> wrote:
>
> What precisely are you trying to compute? Are you trying to find the coefficients of the polynomials in the standard basis? Are you trying to evaluate them at a point?
>
> Note that the LegendreStieltjes polynomials do not satisfy threeterm recurrence relations, and so recursive rules (depending on what precisely you mean by that) are not available.
>
> Nick
>
> â€â€â€â€â€â€â€ Original Message â€â€â€â€â€â€â€
> On Wednesday, February 19, 2020 12:07 PM, N A via Boostusers <boostusers_at_[hidden]> wrote:
>
>> Hi,
>>
>> With regard to the article on Boost:
>> [LegendreStieltjes Polynomials  1.66.0](https://www.boost.org/doc/libs/1_66_0/libs/math/doc/html/math_toolkit/sf_poly/legendre_stieltjes.html)
>>
>> LegendreStieltjes Polynomials  1.66.0
>>
>> Can anyone help me to compute the stieltjes polynomials please? I'm coding in VBA and I'm looking for some recursive rules to calculate same.
>>
>> Thanks
>> Vick
>
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