On ignoring the singularity in numerical quadrature
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- by R. K. Miller PDF
- Math. Comp. 25 (1971), 521-532 Request permission
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.References
- Philip J. Davis and Philip Rabinowitz, Ignoring the singularity in approximate integration, J. Soc. Indust. Appl. Math. Ser. B Numer. Anal. 2 (1965), 367–383. MR 195256
- Philip Rabinowitz, Gaussian integration in the presence of a singularity, SIAM J. Numer. Anal. 4 (1967), 191–201. MR 213016, DOI 10.1137/0704018
- Walter Gautschi, Numerical quadrature in the presence of a singularity, SIAM J. Numer. Anal. 4 (1967), 357–362. MR 218014, DOI 10.1137/0704031
- Arthur Sard, Linear approximation, American Mathematical Society, Providence, R.I., 1963. MR 0158203
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Math. Comp. 25 (1971), 521-532
- MSC: Primary 65D30
- DOI: https://doi.org/10.1090/S0025-5718-1971-0301901-5
- MathSciNet review: 0301901