Adaptive integration and improper integrals
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- by Seymour Haber PDF
- Math. Comp. 29 (1975), 806-809 Request permission
Abstract:
Let R be the class of all functions that are properly Riemann-integrable on [0, 1], and let IR be the class of all functions that are properly Riemann-integrable on [a, 1] for all $a > 0$ and for which \[ \lim \limits _{a \to {0^+}} \int _a^1 {f(x)\;dx} \] exists and is finite. There are computational schemes that produce a convergent sequence of approximations to the integral of any function in R; the trapezoid rule is one. In this paper, it is shown that there is no computational scheme that uses only evaluations of the integrand, that is similarly effective for IR.References
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J. R. RICE, A Metalgorithm for Adaptive Quadrature, CSDTR89, Purdue University, March, 1973.
- 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
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Math. Comp. 29 (1975), 806-809
- MSC: Primary 65D30
- DOI: https://doi.org/10.1090/S0025-5718-1975-0375750-X
- MathSciNet review: 0375750