SINGINT: Automatic numerical integration of singular integrands

Abstract We explore the combination of deterministic and Monte Carlo methods to facilitate efficient automatic numerical computation of multidimensional integrals with singular integrands. Two adaptive algorithms are presented that employ recursion and are runtime and memory optimized, respectively. SINGINT, a C implementation of the algorithms, is introduced and its utilization in the calculation of particle scattering amplitudes is exemplified. Title of program: SINGINT Catalogue Id: ADRQ_v1_0 Nature of problem Efficient, robust and automatic numerical computation of multidimensional integrals with singular integrands, for example occurring in the calculation of particle scattering amplitudes in perturbative field theory. Versions of this program held in the CPC repository in Mendeley Data ADRQ_v1_0; SINGINT; 10.1016/S0010-4655(03)00160-7 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)摘要 本研究探讨了确定性数值方法与蒙特卡洛（Monte Carlo）方法的结合，以助力实现对含奇异被积函数的多维积分进行高效、自动化的数值计算。本文提出两种采用递归策略的自适应算法，二者分别针对运行时性能与内存占用进行了优化。本文介绍了上述算法的C语言实现工具SINGINT，并以粒子散射振幅的计算为例，演示了该工具的实际应用场景。 程序名称：SINGINT 目录编号：ADRQ_v1_0 问题描述 本程序用于实现高效、稳健且自动化的含奇异被积函数的多维积分数值计算，此类积分常见于微扰场论中的粒子散射振幅计算场景。 Mendeley数据平台的CPC程序库中收录的本程序版本：ADRQ_v1_0；SINGINT；10.1016/S0010-4655(03)00160-7 本程序源自贝尔法斯特女王大学馆藏的CPC程序库（1969-2019年）。