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@yahoo.com> 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@protonmail.com> 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.

‐‐‐‐‐‐‐ Original Message ‐‐‐‐‐‐‐

On Saturday, February 22, 2020 6:26 AM, N A via Boost-users <boost-users@lists.boost.org> 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!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?ThanksOn Saturday, February 22, 2020, 01:26:11 PM GMT+4, John Maddock via Boost-users <boost-users@lists.boost.org> 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 quadratureformulae." Mathematics of Computation 22.104 (1968): 847-856John.>> Thanks>>>>> On Friday, February 21, 2020, 06:54:27 PM GMT+4, Nick Thompson via> Boost-users <boost-users@lists.boost.org> 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.>> Nick>>>>> ‐‐‐‐‐‐‐ Original Message ‐‐‐‐‐‐‐> On Wednesday, February 19, 2020 12:07 PM, N A via Boost-users> <boost-users@lists.boost.org> wrote:>>> Hi,>>>> With regard to the article on Boost:>> Legendre-Stieltjes Polynomials - 1.66.0>>>>>>>>>>>> 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>>>>>> _______________________________________________> Boost-users mailing list>> _______________________________________________> Boost-users mailing list_______________________________________________Boost-users mailing list