  In Gaussian graphical models, the likelihood equations must typically be
solved iteratively. We investigate two algorithms: A version of iterative
proportional scaling which avoids inversion of large matrices, and an algorithm
based on convex duality and operating on the covariance matrix by neighbourhood
coordinate descent, corresponding to the graphical lasso with zero penalty. For
large, sparse graphs, the iterative proportional scaling algorithm appears
feasible and has simple convergence properties. The algorithm based on
neighbourhood coordinate descent is extremely fast and less dependent on
sparsity, but needs a positive definite starting value to converge. We give an
algorithm for finding such a starting value for graphs with low colouring
number. As a consequence, we also obtain a simplified proof for existence of
the maximum likelihood estimator in such cases.
