  We explains the shifted COCG method which can solve a series of the linear
equations generated by numbers of scaler shifts, without time consuming
matrix-vector operations, except at the only one reference energy. This is a
family of the CG method and sharing the robustness and the capability of the
accuracy estimation. Then shifted COCG is quite useful to calculate the Green's
function of the many-electron Hamiltonian which have very large dimension. We
applied it to the double orbital extended Hubbard model with twelve electrons
on the periodic sqrt(8) x sqrt(8) site system, the dimension of the Hamiltonian
equals to 64,128,064, and found the ground state is insulator. We also
explained the crucial points of the shifted COCG algorithm for reducing the
amount of required memory.

Strongly Correlated Electrons