## Online material

### Appendix A: Iterative maximization approach

We assume that the optimal model point position is shifted by some small distance,
*δ**φ*_{i},
relative to the grid point location found using RMCLEAN,
(A.1)The ML solution is
obtained by minimizing *H* in Eq. (4) with respect to
*δ**φ*_{i}, which gives
(A.2)where
is the same as ,
Eq. (2), except that the sum is over
*k* ≠ *i*. The operator ℜ selects the real part of its
argument. This expression cannot be solved analytically for
*δ**φ*_{i}, but we can use it
to search for the solutions iteratively. To do so we Taylor expand the exponential term
in Eq. (A.2) to first order, thereby
making *H* second order in
*δ**φ*_{i}. This gives
(A.3)which we can rewrite in
the form (A.4)where
(A.5)We
must also solve for an updated flux. We can again extremize Eq. (4), this time with respect to
*m*_{i}. We find
(A.6)and
thus
(A.7)In our example
implementation, we solve for *δφ* and *m* iteratively
until convergence is achieved. We also attempt to merge nearby model components to
reduce the degrees of freedom in the model according to the prescription described in
Sect. 2.

We tried other iterative schemes, e.g. solving for position and flux changes by
inverting the Hessian matrix of *H*, but found that the approach given
here is the most stable.

*© ESO, 2013*