### Abstract

Original language | English |
---|---|

Pages (from-to) | 2168-2173 |

Number of pages | 6 |

Journal | Computer physics communications |

Volume | 182 |

Issue number | 10 |

DOIs | |

Publication status | Published - 1 Oct 2011 |

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### Keywords

- Condensed Matter - Strongly Correlated Electrons, Physics - Computational Physics

### Cite this

*Computer physics communications*,

*182*(10), 2168-2173. https://doi.org/10.1016/j.cpc.2011.05.016

**A numerical projection technique for large-scale eigenvalue problems.** / Gamillscheg, Ralf; Haase, Gundolf; von der Linden, Wolfgang.

Research output: Contribution to journal › Article › Research › peer-review

*Computer physics communications*, vol. 182, no. 10, pp. 2168-2173. https://doi.org/10.1016/j.cpc.2011.05.016

}

TY - JOUR

T1 - A numerical projection technique for large-scale eigenvalue problems

AU - Gamillscheg, Ralf

AU - Haase, Gundolf

AU - von der Linden, Wolfgang

N1 - arXiv: 1008.1208

PY - 2011/10/1

Y1 - 2011/10/1

N2 - We present a new numerical technique to solve large-scale eigenvalue problems. It is based on the projection technique, used in strongly correlated quantum many-body systems, where first an effective approximate model of smaller complexity is constructed by projecting out high energy degrees of freedom and in turn solving the resulting model by some standard eigenvalue solver. Here we introduce a generalization of this idea, where both steps are performed numerically and which in contrast to the standard projection technique converges in principle to the exact eigenvalues. This approach is not just applicable to eigenvalue problems encountered in many-body systems but also in other areas of research that result in large scale eigenvalue problems for matrices which have, roughly speaking, mostly a pronounced dominant diagonal part. We will present detailed studies of the approach guided by two many-body models.

AB - We present a new numerical technique to solve large-scale eigenvalue problems. It is based on the projection technique, used in strongly correlated quantum many-body systems, where first an effective approximate model of smaller complexity is constructed by projecting out high energy degrees of freedom and in turn solving the resulting model by some standard eigenvalue solver. Here we introduce a generalization of this idea, where both steps are performed numerically and which in contrast to the standard projection technique converges in principle to the exact eigenvalues. This approach is not just applicable to eigenvalue problems encountered in many-body systems but also in other areas of research that result in large scale eigenvalue problems for matrices which have, roughly speaking, mostly a pronounced dominant diagonal part. We will present detailed studies of the approach guided by two many-body models.

KW - Condensed Matter - Strongly Correlated Electrons, Physics - Computational Physics

U2 - 10.1016/j.cpc.2011.05.016

DO - 10.1016/j.cpc.2011.05.016

M3 - Article

VL - 182

SP - 2168

EP - 2173

JO - Computer physics communications

JF - Computer physics communications

SN - 0010-4655

IS - 10

ER -