Hi,Do you have a documentation about the Gauss-Patterson integration method? (how to generate the quadrature points)All i can find in internet is 127 points nothing more!Thx

Can't see why you can't use Gauss-Legendre or Clenshaw-Curtis where the points and weights can be more easily calculated

I heard someone say that Gauss-Kronrod was cool as well...

The Gauss-Patterson rule is found in QUADPACK's QNG algortihm. The quadpack manual has some discussion on the rule, seems that Patterson takes a Gauss-Legendre rule and constructs a nested sequence of rules each of which is an optimal extension of the previous. The purpose of the optimal extension is to provide and error estimate without too much additional computational cost and is similar in nature to a Gauss-Konrod rule. The QNG algorithm has a specific sequence of rules (21,43 & 87 points rules). I have not attempted to compute addition rules, however the papers referred to in the quadpack manual are Patterson, T.N.L (1968), "The optimal addition of points to quadrature formula", Math. Comp., 22, 847-856Piessens, R and Branders, M (1974), "A note on the optimal addition of abscissas to quadrature formulas of Gauss and Lobatto Type", Math. Comp., 28, 135-139

Thank you for your answers.Indeed Gauss-Patterson generalises in someway Gauss-Kronrod. These two methods allows for some error measure.This "property" helps one make a quadrature adaptive.In some cases one needs higher dimension rules. for eg a 255 points Gauss Patterson rule. Those weights and points are hard to find in the net.