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 目录编号：ABBL 程序获取渠道：爱尔兰北爱尔兰贝尔法斯特女王大学计算机物理通讯（CPC Program Library）程序库（见本期申请表单） 适用计算机：FACOM M-780/20；安装单位：日本福冈县东区箱崎九州大学，邮编812 操作系统：IV/F4 使用编程语言：FORTRAN 77 所需高速存储空间：264千字节 字节位数：8 使用的其他外设：读卡机、行式打印机 程序与测试穿孔卡片组总卡片数：…… 程序名称：GAUSSH 目录编号：ABBL_v1_0 问题本质 在物理问题研究中，常需开展定积分的数值求值工作。高斯求积（Gaussian quadrature）是目前公认的最高效的求积方案之一。本程序可快速生成适用于形如∫(-∞,+∞) e^(-x²)f(x)dx 型积分的高斯-埃尔米特求积公式（Gauss-Hermite quadrature formulas）的求积节点与权重，即便求积节点数量极多，仍可保证高精度计算结果。 本程序存放在Mendeley数据的CPC仓库中的版本为： 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维护的CPC程序库（1969-2019）