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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Two formulas for numerical indefinite integration


Author: Seymour Haber
Journal: Math. Comp. 60 (1993), 279-296
MSC: Primary 65D32; Secondary 41A55
MathSciNet review: 1149292
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Abstract: We derive two formulas for approximating the indefinite integral over a finite interval. The approximation error is $ O({c^{ - c\sqrt m }})$ uniformly, where m is the number of integrand evaluations. The integrand is required to be analytic in the interior of the integration interval, but may be singular at the endpoints. Some sample calculations indicate that the actual convergence rate accords with the error bound derived.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1993-1149292-9
PII: S 0025-5718(1993)1149292-9
Article copyright: © Copyright 1993 American Mathematical Society