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

 

Numerical indefinite integration of functions with singularities


Authors: Aeyoung Park Jang and Seymour Haber
Journal: Math. Comp. 70 (2001), 205-221
MSC (2000): Primary 65D30; Secondary 41A55
Published electronically: March 3, 2000
MathSciNet review: 1709152
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Abstract | References | Similar Articles | Additional Information

Abstract: We derive an indefinite quadrature formula, based on a theorem of Ganelius, for $H^p$ functions, for $p>1$, over the interval $(-1,1)$. The main factor in the error of our indefinite quadrature formula is $O(e^{-\pi \sqrt{N/ q}})$, with $2 N $ nodes and $\frac 1 p +\frac 1q=1$. The convergence rate of our formula is better than that of the Stenger-type formulas by a factor of $\sqrt{2}$ in the constant of the exponential. We conjecture that our formula has the best possible value for that constant. The results of numerical examples show that our indefinite quadrature formula is better than Haber's indefinite quadrature formula for $H^p$-functions.


References [Enhancements On Off] (What's this?)

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Additional Information

Aeyoung Park Jang
Affiliation: Trinity College, 10505 Oakton Ridge Court, Oakton, Virginia 22124
Email: aeyoung@prodigy.net

Seymour Haber
Affiliation: Temple University, Mosaryk 1, Jerusalem, Israel

DOI: http://dx.doi.org/10.1090/S0025-5718-00-01226-6
PII: S 0025-5718(00)01226-6
Keywords: Indefinite quadrature formula, $H^p$ functions, singularity
Received by editor(s): May 19, 1998
Received by editor(s) in revised form: January 4, 1999
Published electronically: March 3, 2000
Article copyright: © Copyright 2000 American Mathematical Society