Calculation of Gauss-Kronrod quadrature rules

@article{Laurie1997CalculationOG,
  title={Calculation of Gauss-Kronrod quadrature rules},
  author={Dirk Laurie},
  journal={Math. Comput.},
  year={1997},
  volume={66},
  pages={1133-1145}
}
The Jacobi matrix of the (2n+1)-point Gauss-Kronrod quadrature rule for a given measure is calculated efficiently by a five-term recurrence relation. The algorithm uses only rational operations and is therefore also useful for obtaining the Jacobi-Kronrod matrix analytically. The nodes and weights can then be computed directly by standard software for Gaussian quadrature formulas. 
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