为统计人员定制的高斯求积

摘要：

Gautschi在2004年的专著中描述了定制高斯求积的理论和计算方法。Gautschi还提供了Fortran和MATLAB代码来实现和说明这些方法。我们已经编写了一个R包，在R包Rmpfr提供的高精度算法中实现，它使用基于矩的方法通过矩行列式计算高斯求积规则，最多有33个节点，前提是可以使用Rmpfr包提供的标准数学函数将矩计算到任意精度。我们希望，我们提供的免费R软件包和我们提供的数值结果将鼓励其他统计学家也考虑高斯求积规则的定制构造。

英文摘要：

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.

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