  The large moment method can be used to compute a large number of moments of
physical quantities that are described by coupled systems of linear
differential equations. Besides these systems the algorithm requires a certain
number of initial values as input, that are often hard to derive in a
preprocessing step.Thus a major challenge is to keep the number of initial
values as small as possible. We present the basic ideas of the underlying large
moment method and present refined versions that reduce significantly the number
of required initial values.
