Linear Algebraic Calculation of Green's function for Large-Scale Electronic Structure Theory

A linear algebraic method named the shifted conjugate-orthogonal-conjugate-gradient method is introduced for large-scale electronic structure calculation. The method gives an iterative solver algorithm of the Green's function and the density matrix without calculating eigenstates.The problem is reduced to independent linear equations at many energy points and the calculation is actually carried out only for a single energy point. The method is robust against the round-off error and the calculation can reach the machine accuracy. With the observation of residual vectors, the accuracy can be controlled, microscopically, independently for each element of the Green's function, and dynamically, at each step in dynamical simulations. The method is applied to both semiconductor and metal.Comment: 10 pages, 9 figures. To appear in Phys. Rev. B. A PDF file with better graphics is available at http://fujimac.t.u-tokyo.ac.jp/lses

Primary cardiac osteosarcoma in a 42-year-old woman

We describe here a 42-year-old woman who was admitted to hospital with a pedunculated mass in her left atrium. She was diagnosed with a primary cardiac osteosarcoma with special immunohistochemical characteristics. Echocardiography and computed tomography can be used to differentiate cardiac osteosarcomas from routine intracardiac tumors. The patient was treated by surgical removal of the mass. Two years later, she has shown no evidence of disease recurrence. We discuss primary osteosarcomas in the cardiac cavity and their management