Abscissae and weights for the Gauss-Hermite quadrature formula

Abstract Title of program: GAUSSH Catalogue number: ABBL Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland (see application form in this issue) Computer: FACOM M-780/20; Installation: Kyushu University, Hakozaki, Higashi-ku, Fukuoka 812, Japan Operating system: IV/F4 Programming language used: FORTRAN 77 High speed storage required: 264 Kbytes No. of bits in a byte: 8 Other peripherals used: card reader, line printer No. of cards in combined program and test deck:... Title of program: GAUSSH Catalogue Id: ABBL_v1_0 Nature of problem In the study of physical problems, the need often arises for evaluating definite integrals numerically. The Gaussian quadrature is known as one of the most efficient quadrature schemes. The present program generates the abscissae and weights for the Gauss-Hermite quadrature formulas for integrals of the form integral (-infinity, +infinity) e^-x^2 f(x)dx very rapidly and with high accuracy even in the case of a great many abscissae. Versions of this program held in the CPC repository in Mendeley Data ABBL_v1_0; GAUSSH; 10.1016/0010-4655(88)90046-X This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)摘要 程序名称：GAUSSH 目录号：ABBL 程序获取途径：北爱尔兰贝尔法斯特女王大学CPC程序库（详见本期申请表） 适用计算机：FACOM M-780/20 安装地点：日本福冈市东区箱崎九州大学（邮编812） 操作系统：IV/F4 所用编程语言：FORTRAN 77 所需高速存储空间：264 KB 字节位数：8 配套外设：卡片阅读器、行式打印机 程序与测试卡组总卡片数：…… 程序名称：GAUSSH 目录编号：ABBL_v1_0 问题本质 在物理问题研究中，常需对定积分开展数值求值。高斯求积是当前公认的最高效求积策略之一。本程序可快速生成针对形如∫(-∞,+∞) e^(-x²)f(x)dx型积分的高斯-埃尔米特（Gauss-Hermite）求积公式的求积节点（abscissae）与权重（weights），即便节点数量极多，仍可保证极高的计算精度。 本程序在Mendeley数据的CPC仓库中的版本： ABBL_v1_0; GAUSSH; 10.1016/0010-4655(88)90046-X 本程序源自贝尔法斯特女王大学托管的CPC程序库（1969-2019）