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Authors
Hoshi, Takeo Department of Applied Mathematics and Physics, Tottori University Researchers DB 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
Keywords
Numerical linear algebra
Shifted linear equations
Krylov subspace method
Quantum lattice models
Abstract
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.
Publisher
Elsevier
Content Type
Journal Article
Link
ISSN
00104655
Journal Title
Computer Physics Communications
Volume
258
Published Date
2021-01-31
Publisher-DOI
Text Version
Publisher
Rights
© 2020 The Authors. Published by Elsevier B.V. http://creativecommons.org/licenses/by/4.0/
Citation
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.
Department
Faculty of Engineering/Graduate School of Engineering
Language
English
pii
S0010-4655(20)30255-1