All algorithms have the following properties.
They use the tensor method to approximate the conditional expectation with orthogonal Chebyshev polynomials. The coefficients of the approximating function are such that they minimize the distance between the approximating function and the numerically calculated conditional expectation at a set of grid points. The grid points are Chebyshev nodes. The numerical integration procedure used to calculate the conditional expectation is Hermite Gaussian Quadrature. In my experience it is easier to obtain an accurate solution fast with quadrature methods than with Monte Carlo methods.