# Boost Users :

From: N A (testrope_at_[hidden])
Date: 2020-02-26 05:27:37

Hi,
I haven't heard from you. I hope all is well?
When you get the time, please check x=0.2 and n=6,7 & 8 for me.
Thanks

On Monday, February 24, 2020, 10:25:20 AM GMT+4, N A <testrope_at_[hidden]> wrote:

I've been able to go through the paper and I have potentially succeeded in calculating the coefficients by means of Gaussian elimination. But I want to make sure, I got it right!
So can you please check for me x=0.2 and n=6,7,8?
Thanks a lot!Vick

On Saturday, February 22, 2020, 06:11:33 PM GMT+4, Nick Thompson <nathompson7_at_[hidden]> wrote:

> Does this mean that we can generate different Stieltjes polynomials with different orthogonal polynomials and/or functions?

Yes, you can expand every polynomial in every other complete polynomial basis. The basis you select should make the conversion from the original basis well-conditioned.

â€â€â€â€â€â€â€ Original Message â€â€â€â€â€â€â€
On Saturday, February 22, 2020 6:26 AM, N A via Boost-users <boost-users_at_[hidden]> wrote:

What is the "triangular system of equations" that need to be solved? And how to solve it?

I'm not familiar with these terms!Â

However, I came across another article beside yours that dealt with Stieltjes polynomials. Yours deal with Legendre polynomials-Stieltjes polynomials, but theirs deal with Legendre function of the second kind with regard to Stieltjes polynomials.

They have a mathematica code, which I don't quite understand but their code yields 1.08169 for the same n and x as below.

Does this mean that we can generate different Stieltjes polynomials with different orthogonal polynomials and/or functions?

Can you help me out please?
Thanks

On Saturday, February 22, 2020, 01:26:11 PM GMT+4, John Maddock via Boost-users <boost-users_at_[hidden]> wrote:

On 22/02/2020 03:25, N A via Boost-users wrote:
> Hi
>
> The Legendre polynomials (Lp) of degree n=5 and x=0.2 is 0.30752 and
> according to Boost article, the Legendre-Stieltjes 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?

Please see Patterson, TNL. "The optimum addition of points to quadrature
formulae." Mathematics of Computation 22.104 (1968): 847-856

John.

>
> Thanks
>
>
>
>
> On Friday, February 21, 2020, 06:54:27 PM GMT+4, Nick Thompson via
> Boost-users <boost-users_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 Legendre-Stieltjes polynomials do not satisfy three-term
> recurrence relations, and so recursive rules (depending on what
> precisely you mean by that) are not available.
>
> Â Â  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 Boost-users
> <boost-users_at_[hidden]> wrote:
>
>> Hi,
>>
>> With regard to the article on Boost:
>> Legendre-Stieltjes Polynomials - 1.66.0

>>
>>
>> Â Â Â
>>
>>
>>Â  Â  Legendre-Stieltjes 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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