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2.5.3 Quasi Newton     continued...

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 :