mrowell

12-17-2003, 03:36 PM

Hi

I am attempting to create Gauss Kronrod abcissa and weights where the orthogonal polynomials are Legendre. (a la quadpack I think). I am using a technique described by Dirk Laurie 'Calculation of Gauss-Kronrod Quadrature Rules' to create the recursion cofficients a and b as described in eq 4.5.6 and 4.5.7 of section 4.5. Anyway after that long introduction, I cannot get the a's to eb anything other than 0.

Here are my steps

(1) Taking normal Legendre polynomials I make the "monic"

(2) then attempting to calculate the a values for some j I integrate

x * pj(x) * pj(x) between the limits -1 to 1. (I omitted W(x) the weight function as this is 1 for Legendre polynomials)

(3) I always get 0 for this....

Am I performing the scalar product i.e. <xp(j)|p(j)> wrong?

Hoping someone can help...

P.S. Cannot use quadpack as my language is Java and I do not want to translate it by hand. I know there is a tool f2j out there but I have had limited success with it in the past.

Regards

Mark

I am attempting to create Gauss Kronrod abcissa and weights where the orthogonal polynomials are Legendre. (a la quadpack I think). I am using a technique described by Dirk Laurie 'Calculation of Gauss-Kronrod Quadrature Rules' to create the recursion cofficients a and b as described in eq 4.5.6 and 4.5.7 of section 4.5. Anyway after that long introduction, I cannot get the a's to eb anything other than 0.

Here are my steps

(1) Taking normal Legendre polynomials I make the "monic"

(2) then attempting to calculate the a values for some j I integrate

x * pj(x) * pj(x) between the limits -1 to 1. (I omitted W(x) the weight function as this is 1 for Legendre polynomials)

(3) I always get 0 for this....

Am I performing the scalar product i.e. <xp(j)|p(j)> wrong?

Hoping someone can help...

P.S. Cannot use quadpack as my language is Java and I do not want to translate it by hand. I know there is a tool f2j out there but I have had limited success with it in the past.

Regards

Mark