  On a domain of the n-dimensional Euclidean space, and for an integer
k=1,...,n, the k-Hessian equations are fully nonlinear elliptic equations for k
>1 and consist of the Poisson equation for k=1 and the Monge-Ampere equation
for k=n. We analyze for smooth non degenerate solutions a 9-point finite
difference scheme. We prove that the discrete scheme has a locally unique
solution with a quadratic convergence rate. In addition we propose new
iterative methods which are numerically shown to work for non smooth solutions.
A connection of the latter with a popular Gauss-Seidel method for the
Monge-Ampere equation is established and new Gauss-Seidel type iterative
methods for 2-Hessian equations are introduced.
