10.17632/MT928NZ5R3.1
Hoshi, Takeo
Takeo
Hoshi
Kω - Open-source library for the shifted Krylov subspace method of the form (zI - H)x = b
Mendeley
2020
Dataset
Numerical Linear Algebra
Computational Physics
Kawamura, Mitsuaki
Mitsuaki
Kawamura
Yoshimi, Kazuyoshi
Kazuyoshi
Yoshimi
Motoyama, Yuichi
Yuichi
Motoyama
Misawa, Takahiro
Takahiro
Misawa
Yamaji, Youhei
Youhei
Yamaji
Todo, Synge
Synge
Todo
Kawashima, Naoki
Naoki
Kawashima
Sogabe, Tomohiro
Tomohiro
Sogabe
2020-08-19
10.1016/j.cpc.2020.107536
10.17632/mt928nz5r3
GNU Lesser General Public License
We develop Kω, an open-source linear algebra library for the shifted Krylov subspace methods. The methods solve a set of shifted linear equations (z_k I - H)x^(k) = b (k = 0, 1, 2, ...) for a given matrix H and a vector b, simultaneously. The leading order of the operational cost is the same as that for a single equation. The shift invariance of the Krylov subspace is the mathematical foundation of the shifted Krylov subspace methods. Applications in materials science are presented to demonstrate the advantages of the algorithm over the standard Krylov subspace methods such as the Lanczos method. We introduce benchmark calculations of (i) an excited (optical) spectrum and (ii) intermediate eigenvalues by the contour integral on the complex plane. In combination with the quantum lattice solver HΦ, Kω can realize parallel computation of excitation spectra and intermediate eigenvalues for various quantum lattice models.