Numerical indefinite integration of functions with singularities
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- by Aeyoung Park Jang and Seymour Haber;
- Math. Comp. 70 (2001), 205-221
- DOI: https://doi.org/10.1090/S0025-5718-00-01226-6
- Published electronically: March 3, 2000
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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 Haberβs indefinite quadrature formula for $H^p$-functions.References
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Bibliographic 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
- Received by editor(s): May 19, 1998
- Received by editor(s) in revised form: January 4, 1999
- Published electronically: March 3, 2000
- © Copyright 2000 American Mathematical Society
- Journal: Math. Comp. 70 (2001), 205-221
- MSC (2000): Primary 65D30; Secondary 41A55
- DOI: https://doi.org/10.1090/S0025-5718-00-01226-6
- MathSciNet review: 1709152