Comparison of Three High-Precision Quadrature Schemes.

Bailey, D. H. ; Li, X. S.

Technical Information Center Oak Ridge Tennessee

关键词: Accuracy;    Performance;    Quadratures;    Numerical quadrature;    Arbitrary precision arithmetic;   

RP-ID  :  DE2004822964

学科分类：工程和技术（综合）

美国|英语

来源: National Technical Reports Library

【 摘 要 】

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.