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An efficient parallel algorithm is presented and tested for computing selected components of H −1 where H has the structure of a Hamiltonian matrix of two-dimensional lattice models with local interaction. Calculations of this type are useful for several applications, including electronic structure analysis of materials in which the diagonal elements of the Green's functions are needed. The algorithm proposed here is a direct method based on an LDL T factorization. The elimination tree is useddoi:10.1137/09077432x fatcat:6gt5l5eqojaxxmh56snnseh7ci