# 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} }

- Published 1997 in Math. Comput.
DOI:10.1090/S0025-5718-97-00861-2

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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