A numerical projection technique for large-scale eigenvalue problems

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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.
Original languageEnglish
Pages (from-to)2168-2173
Number of pages6
JournalComputer physics communications
Volume182
Issue number10
DOIs
Publication statusPublished - 1 Oct 2011

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eigenvalues
projection
degrees of freedom
matrices
energy

Keywords

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

Cite this

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

In: Computer physics communications, Vol. 182, No. 10, 01.10.2011, p. 2168-2173.

Research output: Contribution to journalArticleResearchpeer-review

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