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