hermite_rule, a C code which generates a specific Gauss-Hermite quadrature rule.
The rule is written to three files for easy use as input to other programs.
The Gauss-Hermite quadrature rule is used as follows:
c * Integral ( -oo < x < +oo ) f(x) exp ( - b * ( x - a )^2 ) dx
is to be approximated by
Sum ( 1 <= i <= order ) w(i) * f(x(i))
Generally, a Gauss-Hermite quadrature rule of n points will
produce the exact integral when f(x) is a polynomial of degree
2n-1 or less.
The value of C in front of the integral depends on the user's choice of the SCALE parameter:
hermite_rule order a b scale filenamewhere
The information on this web page is distributed under the MIT license.
hermite_rule is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and a Octave version and a Python version.
c_rule, a C code which computes a quadrature rule which estimates the integral of a function f(x), which might be defined over a one dimensional region (a line) or more complex shapes such as a circle, a triangle, a quadrilateral, a polygon, or a higher dimensional region, and which might include an associated weight function w(x).
hermite_exactness, a C code which tests the polynomial exactness of Gauss-Hermite quadrature rules for estimating the integral of a function with density exp(-x^2) over the interval (-oo,+oo).
quadrature_rules_hermite_physicist, a dataset directory which contains Gauss-Hermite quadrature rules, for integration on the interval (-oo,+oo), with weight function exp(-x^2).
quadrature_rules_hermite_probabilist, a dataset directory which contains Gauss-Hermite quadrature rules, for integration on the interval (-oo,+oo), with weight function exp(-x^2/2).
quadrature_rules_hermite_unweighted, a dataset directory which contains Gauss-Hermite quadrature rules, for integration on the interval (-oo,+oo), with weight function 1.