How to Calculate Weights for Gauss-Kronrod Quadrature Using Nodes and Degree?

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SUMMARY

The Gauss-Kronrod quadrature employs the zeros of Legendre Polynomials of degree n and Stieltjes Polynomials of degree n+1 to determine nodes for integration. Specifically, using the Gauss polynomial of degree 7 necessitates the Stieltjes polynomial of degree 8, resulting in a total of 15 nodes according to the quadrature rule (2n+1). The discussion highlights the challenge of calculating weights from these nodes, contrasting it with the more straightforward process of determining weights for Gauss-Legendre quadrature.

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TL;DR
How to compute the weights once you have the nodes?
The Gauss-Kronrod quadrature uses the zeros of the Legendre Polynomials of degree n and the zeros of the Stieltjes polynomials of degree n+1. These zeros are the nodes for the quadrature. For example using the Gauss polynomial of degree 7, you will need the Stieltjes of degree 8 and both makes up to 15 nodes in accordance to the quadrature rule (2n+1).

But how would you calculate the weights given the nodes and the degree?
 
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Try Google for Gauss-Kronrod.
 
mathman said:
Try Google for Gauss-Kronrod.
I tried but nothing comes in handy.

For example the Gauss-Legendre quadrature weights is easily understood in this link: Legendre weights
So I'm looking for something like this for the Gauss-Kronrod!
 

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