Abstract
A scheme for a fast decomposition of the total density of states evaluated by the recursion method is presented. It is suggested that all the projected densities can be obtained in a single recursion calculation instead of applying the complete recursion procedure to each projection separately. The proposed scheme appears to be exact for the correct choice of the initial vector of the recursion transformation. It is shown that when the random initial vector approach to the total density of states is implemented, good results can be obtained, in particular for calculating the partial densities of states. The applicability and efficiency of the proposed method are demonstrated on two model systems. A simple criterion of reliability is formulated. Possible ways to eliminate spurious effects caused by the random initial vector approach are discussed.

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