AI 中文总结
本文提出一种将交错级数改写为带Abel权重的加权积分后用sinc规则求和的简单算法，通过数值实验验证了误差估计的可靠性，相关Matlab代码为开源软件。
AI 中文摘要
本文研究一般项可通过解析函数表示的交错级数的和的计算问题。在将该级数重写为带有Abel权重的加权积分后，我们采用sinc（梯形）规则，并针对求积点数量分析余项项。我们开展了若干数值实验，以验证所推导误差估计的可靠性，并测试该用于达到指定精度的自动求和算法。本文所用全部Matlab代码可在作者主页作为开源软件获取。
英文摘要
This paper deals with the computation of the sum of alternating series, whose general terms can be expressed by means of analytic functions. After rewriting the series as a weighted integral with the Abel weight, we employ the sinc (trapezoidal) rule and analyze the remainder term with respect to the number of quadrature points. We provide some numerical experiments to show the reliability of the derived error estimate and to test the algorithm for automatic summation with prescribed accuracy. All the Matlab codes used in the present paper can be found as open-source software at the authors' homepage.
