Modification of the matrix-operator method for solving the equation of radiative transfer

Our proposed method shortens the time needed to calculate the radiation field when the albedo for single scattering is not close to unity. An algorithm is given for reflection-operator calculations in a semi-infinite medium. The reflection and transmission matrices may be expressed in terms of this operator for any value of the optical depth. The calculation time is shorter because the doubling algorithm is reduced to a single matrix multiplication, while in the classical method, five matrix multiplications and one inversion must be carried out for each step of optical-depth doubling.