## Extensions of Gauss Quadrature via Linear ProgrammingE. Ryu and S. Boyd
Gauss quadrature is a well known method for estimating the integral
of a continuous function with respect to a given measure as a
weighted sum of the function evaluated at a set of node points.
Gauss quadrature is traditionally developed using orthogonal polynomials.
We show that Gauss quadrature can also be obtained
as the solution to an infinite dimensional linear program:
Minimize the th moment,
among all nonnegative measures that match the |