Since each gradient difference provides
information about one * column* of , we attempt
to construct a family of successive approximation matrices
so that, if were a
constant, the procedure would be consistent with equation (52).
This forms the basis for the * QN condition* on
the new update, :

To specify uniquely additional conditions are required.
For instance, it is
reasonable to assume that differs from by a
* low rank*
`updating' matrix (i.e., a matrix of rank much less than **n**) that
depends on , , and possibly :