• Corpus ID: 210860793

K$\omega$ -- Open-source library for the shifted Krylov subspace method of the form $(zI-H)x=b$

@article{Hoshi2020KomegaO,
  title={K\$\omega\$ -- Open-source library for the shifted Krylov subspace method of the form \$(zI-H)x=b\$},
  author={Takeo Hoshi and Mitsuaki Kawamura and Kazuyoshi Yoshimi and Yuichi Motoyama and Takahiro Misawa and Youhei Yamaji and Synge Todo and Naoki Kawashima and Tomohiro Sogabe},
  journal={arXiv: Numerical Analysis},
  year={2020}
}
We develop K$\omega$, 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… 

Figures and Tables from this paper

References

SHOWING 1-9 OF 9 REFERENCES

Computing 70

  • 87
  • 2003

Numerical Analysis

Electron

Trans

JSIAM Letters 2

  • 127
  • 2010

East Asia J

  • on Appl. Math. 1, 97
  • 2011

Solid State Phys

  • 35, 215
  • 1980

SIAM J

  • on Sci. Comput. 38, A302
  • 2016

Commun

  • 1, 045010
  • 2017