A Comparison of three high-precision quadrature schemes

Conference · Tue Jul 01 04:00:00 EDT 2003

OSTI ID:822964

Bailey, David H ^[1]; Li, Xiaoye S

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1. LBNL Library

The authors have implemented three numerical quadrature schemes, using the new Arbitrary Precision (ARPREC) software package, with the objective of seeking a completely ''automatic'' arbitrary precision quadrature facility, namely one that does not rely on a priori information of the function to be integrated. Such a facility is required, 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 vertical derivatives and integrable singularities at endpoints, as well as several integrals on an infinite interval.

• Research Organization: Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, CA (US)
• Sponsoring Organization: USDOE Director, Office of Science. Office of Advanced Scientific Computing Research. Mathematical, Information, and Computational Sciences Division (US)
• DOE Contract Number: AC03-76SF00098
• OSTI ID: 822964
• Report Number(s): LBNL--53652
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ACCURACY
ARBITRARY PRECISION ARITHMETIC QUADRATURE
PERFORMANCE
QUADRATURES