Effective Bounds in Euler-Maclaurin-Based Quadrature (Summary for HPCS06)
Effective Bounds in Euler-Maclaurin-Based Quadrature (Summary for HPCS06)
复制标题
基于欧拉-麦克劳林求积的有效界（HPCS06 的摘要）
DOI：
--
复制
发表时间：
2006
期刊：
影响因子：
--
通讯作者：
J. Borwein
中科院分区：
文献类型：
--
作者：
D. Bailey;J. Borwein
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.
