论文标题
统计学家的定制高斯正交
Custom-made Gauss quadrature for statisticians
论文作者
论文摘要
定制高斯正交的理论和计算方法已在Gautschi的2004年专着中进行了描述。 Gautschi还为实现和说明了这些方法提供了FORTRAN和MATLAB代码。我们编写了一个R软件包，该软件包在由R软件包RMPFR提供的高精度算术中实现，该软件包通过MONM SECASTINS使用基于矩的方法来计算具有最高33个节点的高斯正交规则，前提是可以使用RMPFR包提供的标准数学功能将矩计算为任意精度。我们的希望是，我们的免费R包以及我们提出的数值结果将鼓励其他统计学家也考虑了高斯正交规则的定制构造。
The theory and computational methods for custom-made Gauss quadrature have been described in Gautschi's 2004 monograph. Gautschi has also provided Fortran and MATLAB code for the implementation and illustration of these methods. We have written an R package, implemented in the high-precision arithmetic provided by the R package Rmpfr, that uses a moment-based method via moment determinants to compute a Gauss quadrature rule, with up to 33 nodes, provided that the moments can be computed to arbitrary precision using the standard mathematical functions provided by the Rmpfr package. Our hope is that the provision of our free R package and the numerical results that we present will encourage other statisticians to also consider the custom-made construction of Gauss quadrature rules.
