フルテキストファイル
著者
星 健夫 Department of Applied Mathematics and Physics, Tottori University 研究者総覧 KAKEN
Kawamura, Mitsuaki Institute for Solid State Physics, University of Tokyo
Yoshimi, Kazuyoshi Institute for Solid State Physics, University of Tokyo
Motoyama, Yuichi Institute for Solid State Physics, University of Tokyo
Misawa, Takahiro Institute for Solid State Physics, University of Tokyo
Yamaji, Youhei Department of Applied Physics, University of Tokyo
Todo, Synge Department of Physics, University of Tokyo / Institute for Solid State Physics, University of Tokyo
Kawashima, Naoki Institute for Solid State Physics, University of Tokyo
Sogabe, Tomohiro Department of Applied Physics, Nagoya University
キーワード
Numerical linear algebra
Shifted linear equations
Krylov subspace method
Quantum lattice models
抄録
We develop Kω, an open-source linear algebra library for the shifted Krylov subspace methods. The methods solve a set of shifted linear equations (zkI−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.
出版者
Elsevier
資料タイプ
学術雑誌論文
外部リンク
ISSN
00104655
掲載誌名
Computer Physics Communications
258
発行日
2021-01-31
出版者DOI
著者版フラグ
出版社版
著作権表記
© 2020 The Authors. Published by Elsevier B.V. http://creativecommons.org/licenses/by/4.0/
掲載情報
Hoshi, Takeo. Kawamura, Mitsuaki. Yoshimi, Kazuyoshi. et al. Kω — Open-source library for the shifted Krylov subspace method of the form (zI−H)x=b. Computer Physics Communications. 258. 107536. 2021-01-31.
部局名
工学部・工学研究科
言語
英語
pii
S0010-4655(20)30255-1