The complete linearization scheme for solving non-LTE transfer problems is reformulated so that the procedure requires the same amount of computation per iteration as the 'equivalent-two-level-atom' approach. The reformulation involves making the timing linearly proportional to the number of frequencies; the resulting system of equations may be solved by a simple block iterative method. It is noted that this reformulation has the same asymptotic timing as integral-equation methods but retains the flexibility and self-consistency of the original complete linearization scheme. The proposed technique is used to solve a multitransition line-formation problem for a five-level representation of the Ca II ion in the solar chromosphere and to solve the resonance-doublet problem for Na I in the chromosphere.
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Auer et al. (1976) studied this question.