| gaussHermiteData {fastGHQuad} | R Documentation |
Compute Gauss-Hermite quadrature rule
Description
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+.
Usage
gaussHermiteData(n)
Arguments
n |
Order of Gauss-Hermite rule to compute (number of nodes) |
Details
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+.
Value
A list containing:
x |
the n node positions for the requested rule |
w |
the w quadrature weights for the requested rule |
Author(s)
Alexander W Blocker ablocker@gmail.com
References
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.