Adaptive integration and improper integrals
Math. Comp. 29 (1975), 806-809
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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 and for which 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.
- J. R. RICE, A Metalgorithm for Adaptive Quadrature, CSDTR89, Purdue University, March, 1973.
- P. J. DAVIS & P. RABINOWITZ, "Ignoring the singularity in approximate integration," J. Soc. Indust. Appl. Math. Ser. B Numer. Anal., v. 2, 1965, pp. 367-383. MR 33 #3459. MR 0195256 (33:3459)
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