A note on Gauss-Hermite quadrature. (English) Zbl 0813.65053

Liu, Qing; Pierce, Donald A.

Biometrika 81, No. 3, 624-629 (1994).

The Gauss-Hermite formula \(\int^ \infty_{-\infty} f(x) \exp (-x^ 2) dx \approx \sum^ m_{i=1} w_ i f(x_ i)\) will provide only good results, if the integrand is sampled in a reasonable range. To this end some transformations are often necessary. This fact is discussed in this note.

Reviewer: D.Braess (Bochum)

MSC:

65D32	Numerical quadrature and cubature formulas
41A55	Approximate quadratures

Keywords:

Gauss-Hermite quadrature; Gauss-Hermite formula