Gauss-Kronrod quadrature in an adaptive Gaussian quadrature method for numerical integration in which error is estimation based on evaluation at special points known as "Kronrod points." By suitably picking these points, abscissas from previous iterations can be reused as part of the new set of points, whereas usual Gaussian quadrature would require recomputation of all abscissas at each iteration. This is particularly important when some specified degree of accuracy is needed but the number of points needed to achieve this accuracy is not known ahead of time. Kronrod showed how to pick Kronrod points optimally from Legendre-Gauss quadrature, and Patterson (1968, 1969) showed how to compute continued extensions of this kind .
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