There are two major strategies for accepting or discarding fill-in,
one structural, and one numerical. The structural strategy is that of
accepting fill-in only to a certain level. As was already pointed out above,
any zero location 
in 
filling in (say in step 
)
is assigned a fill level value
If 
was already nonzero, the level value is not changed.
The numerical fill strategy is that of `drop tolerances': fill is ignored if it is too small, for a suitable definition of `small'. Although this definition makes more sense mathematically, it is harder to implement in practice, since the amount of storage needed for the factorization is not easy to predict. See [157][20] for discussions of preconditioners using drop tolerances.
