Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

Adaptive integration and improper integrals


Author: Seymour Haber
Journal: Math. Comp. 29 (1975), 806-809
MSC: Primary 65D30
MathSciNet review: 0375750
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

$\displaystyle \mathop {\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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65D30

Retrieve articles in all journals with MSC: 65D30


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1975-0375750-X
PII: S 0025-5718(1975)0375750-X
Keywords: Integrals, improper integrals, numerical analysis, numerical integration, numerical quadrature, quadrature, singularities, Riemann integral
Article copyright: © Copyright 1975 American Mathematical Society