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We explains the shifted COCG method which can solve a series of the linearequations generated by numbers of scaler shifts, without time consumingmatrix-vector operations, except at the only one reference energy. This is afamily of the CG method and sharing the robustness and the capability of theaccuracy estimation. Then shifted COCG is quite useful to calculate the Green'sfunction of the many-electron Hamiltonian which have very large dimension. Weapplied it to the double orbital extended Hubbard model with twelve electronson the periodic sqrt(8) x sqrt(8) site system, the dimension of the Hamiltonianequals to 64,128,064, and found the ground state is insulator. We alsoexplained the crucial points of the shifted COCG algorithm for reducing theamount of required memory.

Shifted COCG method and its application to double orbital extended Hubbard model