  Recently, the regularized functional matching pursuit (RFMP) was introduced
as a greedy algorithm for linear ill-posed inverse problems. This algorithm
incorporates the Tikhonov-Phillips regularization which implies the necessity
of a parameter choice. In this paper, some known parameter choice methods are
evaluated with respect to their performance in the RFMP and its enhancement,
the regularized orthogonal functional matching pursuit (ROFMP). As an example
of a linear inverse problem, the downward continuation of gravitational field
data from the satellite orbit to the Earth's surface is chosen, because it is
exponentially ill-posed. For the test scenarios, different satellite heights
with several noise-to-signal ratios and kinds of noise are combined. The
performances of the parameter choice strategies in these scenarios are
analyzed. For example, it is shown that a strongly scattered set of data points
is an essentially harder challenge for the regularization than a regular grid.
The obtained results yield a first orientation which parameter choice methods
are feasible for the RFMP and the ROFMP.
