Open Access
2005 A comparison of three high-precision quadrature schemes
David H. Bailey, Karthik Jeyabalan, Xiaoye S. Li
Experiment. Math. 14(3): 317-329 (2005).


The authors have implemented three numerical quadrature schemes, using the Arbitrary Precision (ARPREC) software package. The objective here is a quadrature facility that can efficiently evaluate to very high precision a large class of integrals typical of those encountered in experimental mathematics, relying on a minimum of a priori information regarding the function to be integrated. Such a facility is useful, for example, to permit the experimental identification of definite integrals based on their numerical values. The performance and accuracy of these three quadrature schemes are compared using a suite of 15 integrals, ranging from continuous, well-behaved functions on finite intervals to functions with infinite derivatives and blow-up singularities at endpoints, as well as several integrals on an infinite interval. In results using 412-digit arithmetic, we achieve at least 400-digit accuracy, using two of the programs, for all problems except one highly oscillatory function on an infinite interval. Similar results were obtained using 1,012-digit arithmetic.


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David H. Bailey. Karthik Jeyabalan. Xiaoye S. Li. "A comparison of three high-precision quadrature schemes." Experiment. Math. 14 (3) 317 - 329, 2005.


Published: 2005
First available in Project Euclid: 3 October 2005

zbMATH: 1082.65028
MathSciNet: MR2172710

Primary: 65D30

Keywords: arbitrary precision , numerical integration , Numerical quadrature

Rights: Copyright © 2005 A K Peters, Ltd.

Vol.14 • No. 3 • 2005
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