hermite_rule, an Octave code which generates a specific Gauss-Hermite quadrature rule, based on user input.
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 ) dxis 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 'filename' )where
The computer code and data files described and made available on this web page are 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 an Octave version.
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quadrature_rules_hermite_physicis, 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).
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