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Calculation of Gauss-Kronrod quadrature rules


Author: Dirk P. Laurie
Journal: Math. Comp. 66 (1997), 1133-1145
MSC (1991): Primary 65D30, 65D32
DOI: https://doi.org/10.1090/S0025-5718-97-00861-2
MathSciNet review: 1422788
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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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Additional Information

Dirk P. Laurie
Affiliation: Potchefstroom University for Christian Higher Education, P. O. Box 1174, Vanderbiljpark, 1900, South Africa
Email: dlaurie@na-net.ornl.gov

DOI: https://doi.org/10.1090/S0025-5718-97-00861-2
Received by editor(s): June 28, 1995
Received by editor(s) in revised form: November 2, 1995
Article copyright: © Copyright 1997 American Mathematical Society