Calculation of Gauss-Kronrod quadrature rules

Laurie, Dirk

doi:10.1090/S0025-5718-97-00861-2

Calculation of Gauss-Kronrod quadrature rules
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by Dirk P. Laurie PDF

Math. Comp. 66 (1997), 1133-1145 Request permission

Abstract:

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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