Inner Iteration Error in the S_N Algorithm

The discrete ordinates algorithm in plane geometry is formulated within a mathematical framework which allows a detailed analysis of its convergence properties. The infinity norm of the iteration matrix is explicitly calculated for a slab geometry with a homogeneous isotropically scattering medium. This approach permits the calculation of a new convergence criterion which, along with the demonstrated convergence properties of the S_N algorithm, guarantees that the fractional iterative error is arbitrarily small.