Inner iteration error in the S/sub 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 SN algorithm, guarantees that the fractional iterative error is arbitrarily small.