Computes Gauss-Hermite quadrature rule of requested order using Golub-Welsch algorithm. Returns result in list consisting of two entries: x, for nodes, and w, for quadrature weights. This is very fast and numerically stable, using the Golub-Welsch algorithm with specialized eigendecomposition (symmetric tridiagonal) LAPACK routines. It can handle quadrature of order 1000+.
gaussHermiteData(n)Order of Gauss-Hermite rule to compute (number of nodes)
A list containing:
the n node positions for the requested rule
the w quadrature weights for the requested rule
This function computes the Gauss-Hermite rule of order n using the Golub-Welsch algorithm. All of the actual computation is performed in C/C++ and FORTRAN (via LAPACK). It is numerically-stable and extremely memory-efficient for rules of order 1000+.
Golub, G. H. and Welsch, J. H. (1969). Calculation of Gauss Quadrature Rules. Mathematics of Computation 23 (106): 221-230
Liu, Q. and Pierce, D. A. (1994). A Note on Gauss-Hermite Quadrature. Biometrika, 81(3) 624-629.