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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Gauss-Kronrod integration rules for Cauchy principal value integrals


Author: Philip Rabinowitz
Journal: Math. Comp. 41 (1983), 63-78
MSC: Primary 65D30
Corrigendum: Math. Comp. 50 (1988), 655.
Corrigendum: Math. Comp. 50 (1988), 655-657.
MathSciNet review: 701624
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Abstract: Kronrod extensions to two classes of Gauss and Lobatto integration rules for the evaluation of Cauchy principal value integrals are derived. Since in one frequently occurring case, the Kronrod extension involves evaluating the derivative of the integrand, a new extension is introduced using $ n + 2$ points which requires only values of the integrand. However, this new rule does not exist for all n, and when it does, several significant figures are lost in its use.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1983-0701624-2
PII: S 0025-5718(1983)0701624-2
Keywords: Cauchy principal value integral, Kronrod rule, Gauss integration rule, Lobatto integration rule, Gegenbauer polynomials, Szegö polynomials
Article copyright: © Copyright 1983 American Mathematical Society