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Mathematics of Computation

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On ignoring the singularity in numerical quadrature


Author: R. K. Miller
Journal: Math. Comp. 25 (1971), 521-532
MSC: Primary 65D30
DOI: https://doi.org/10.1090/S0025-5718-1971-0301901-5
MathSciNet review: 0301901
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Abstract: This paper studies the convergence of numerical quadratures of singular integrands. The singularities are ignored in the sense that whenever a singularity occurs the integrand is redefined to be zero. Several convergence theorems are proved under the assumption that the integrand can be dominated near each singularity by a monotone, integrable function.


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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1971-0301901-5
Keywords: Quadrature, singular quadrature, singular integrals, ignoring the singularity, error bounds, weak singularity
Article copyright: © Copyright 1971 American Mathematical Society