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A novel linear-algebraic algorithm, multiple Arnoldi method, was developed inan interdisciplinary study between physics and applied mathematics and realizedone-hundred-million-atom (100-nm-scale) electronic state calculations on the Kcomputer. The algorithms are Krylov-subspace solvers for generalized shiftedlinear equations and were implemented in our order-N calculation code ELSES(http://www.elses.jp/). Moreover, a method for calculating eigen states ispresented as a theoretical extension.

Novel linear algebraic theory and one-hundred-million-atom electronic structure calculation on the K computer