For an update of rank one, written as , we
obtain from (53) the condition that
is a vector in the direction
of . This produces the * general rank
one*
update formula as:

for . Broyden's QN method, for example, uses
. While Broyden's update does not guarantee symmetry,
it is useful for solving nonlinear equations and for deriving
a more effective, rank two update.
To restrict the general rank one update form of (53)
further, we can impose the condition of symmetry. Symmetry will be
``inherited'' from to if
for some scalar . Letting that be ,
we obtain the * general symmetric rank 1* update (SR1) as follows:

Now, SR1 will only be positive-definite if . Thus, rank two updates (e.g., ) were thought until very recently to be more suitable for optimization.