A numerical method for calculating the Green's function arising from   electronic structure theory
  We developed a fast numerical methodfor complex symmetric shifted linear systems, which is motivated by the quantum-mechanical (electronic-structure) theory in nanoscale materials. The method is named shifted Conjugate Orthogonal Conjugate Gradient (shifted COCG) method. The formulation is given and several numerical aspects are discussed. 
T. Sogabe, T. Hoshi, S.-L. Zhang, T. Fujiwara