A numerical projection technique for large-scale eigenvalue problems

Publikation: Beitrag in einer FachzeitschriftArtikelForschungBegutachtung

Abstract

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.
Originalspracheenglisch
Seiten (von - bis)2168-2173
Seitenumfang6
FachzeitschriftComputer physics communications
Jahrgang182
Ausgabenummer10
DOIs
PublikationsstatusVeröffentlicht - 1 Okt 2011

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eigenvalues
projection
degrees of freedom
matrices
energy

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

    in: Computer physics communications, Jahrgang 182, Nr. 10, 01.10.2011, S. 2168-2173.

    Publikation: Beitrag in einer FachzeitschriftArtikelForschungBegutachtung

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    abstract = "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.",
    keywords = "Condensed Matter - Strongly Correlated Electrons, Physics - Computational Physics",
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