A new method to calculate the Green function by polynomial expansion

An efficient scheme is introduced to calculate the Green function on the ba sis of polynomials expansion. This scheme has the following advantages: (i) it is possible to calculate both the diagonal and off-diagonal elements of the Green function, (ii) applicable to the system with discrete spectrum, (iii) integrated density of states can also be obtained by the same algorit hm, and (iv) it is suitable for vector and parallel processing, and require d CPU time and memory size are proportional only to the system size (i.e. o rdered N). Applications are made to simple lattice systems for demonstratio n.