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Effective Bounds in Euler-Maclaurin-Based Quadrature (Summary for HPCS06)

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2 Author(s)
Bailey, D.H. ; Lawrence Berkeley National Lab, USA ; Borwein, J.M.

We analyze the behavior of Euler-Maclaurin-based integration schemes with the intention of deriving accurate and economic estimations of the error. These schemes typically provide very high-precision results (hundreds or thousands of digits), in reasonable run time, even in cases where the integrand function has a blow-up singularity or infinite derivative at an endpoint. Heretofore, researchers using these schemes have relied mostly on ad hoc error estimation schemes to project the estimated error of the present iteration. In this paper, we seek to develop some more rigorous, yet highly usable schemes to estimate these errors.

Published in:

High-Performance Computing in an Advanced Collaborative Environment, 2006. HPCS 2006. 20th International Symposium on

Date of Conference:

14-17 May 2006