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.
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
- 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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