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- W2766874295 abstract "A Comparison of Three High-Precision Quadrature Schemes David H. Bailey a , Xiaoye S. Li b , Berkeley National Laboratory, Berkeley, CA 94720. This work is supported by the Director, Office of Computational and Technology Research, Division of Mathematical, Information, and Computational Sciences of the U.S. Department of Energy, under contract number DE-AC03-76SF00098. b Lawrence a Lawrence Berkeley National Laboratory, Berkeley, CA 94720 Abstract 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 inte- grals based on their numerical values. The performance and accuracy of these three quadrature schemes are compared using a suite of 15 integrals, ranging from contin- uous, 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. Key words: numerical quadrature, arbitrary precision Introduction Numerical quadrature has a long and distinguished history, including con- tributions by Newton, who devised the basis of what is now known as the Newton-Cotes scheme, and Gauss, who devised what is now known as Gaus- sian quadrature. In the twentieth century, numerous additional schemes were Email addresses: dhbailey@lbl.gov (David H. Bailey), xsli@lbl.gov (Xiaoye S. Li). Preprint submitted to Real Numbers and Computers’5 5 June 2003" @default.
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- W2766874295 date "2003-07-01" @default.
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- W2766874295 title "A Comparison of three high-precision quadrature schemes - eScholarship" @default.
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