Mathematics of Computation

Author(s): Aeyoung Park Jang; Seymour Haber.
Journal: Math. Comp. 70 (2001), 205-221.
MSC (2000): Primary 65D30; Secondary 41A55
Posted: March 3, 2000
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Abstract: We derive an indefinite quadrature formula, based on a theorem of Ganelius, for

functions, for

, over the interval

. The main factor in the error of our indefinite quadrature formula is $O(e^{-\pi \sqrt{N/ q}})$ , with

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

-functions.

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

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