Generalied Gaussian Quadrature

This package is an implementation of the algorithm presented by Ma et all. in GENERALIZED GAUSSIAN QUADRATURE RULES FOR SYSTEMS OF ARBITRARY FUNCTIONS. Slight modification were made, but the general concept is identical.

Gaussian quadrature is a numerical integration technique integrating polynomials up to order $2n-1$, where $n$ is the order of the quadrature rule, exactly. Generalized gaussian quadrature extends this technique to integrate square-root functions and functions with endpoint-singularities exactly.

The generalized Gaussian quadrature rules of degree n for the system $1, \ln(x), x, x \ln(x), x^2, x^2 \ln(x), \dots, x^n$ can be obtained by

x, w = generalizedquadrature(n::Int)