Problems in transport theory have long presented difficulties to the numerical analyst; a great diversity of methods have been spawned by the efforts of many who have attempted to deal with these difficulties, each usually successful only used in production codes for time independent linear transport problems is the source iteration method. This method consists of iterating the particle density in the transport equation using the result of the previous iteration in the scattering integral term thus reducing the computation at each step to a much simpler streaming calculation. This method generally gives good results when the criticality constant, c, is bounded below one; however, the spectral radius of the iteration map approaches one as c does.