  Conventionally, one calculates a zero in a beta function by computing this
function to a given loop order and solving for the zero. Here we discuss a
different method which is applicable in theories where one can perform a
partial diagrammatic summation to infinite-loop order. We show that this
method, compared with the conventional method, yields much better agreement
with exact results in the case of an asymptotically free gauge theory with
${\cal N}=1$ supersymmetry. Applications to other field theories are also
discussed.
