A method for calculating the eigenvalues of large hermitian matrices by second-order recursion formulae

Ayori Mitsutake, Toshiaki Iitaka, Yuko Okamoto

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4 Citations (Scopus)

Abstract

A general discussion of a method for solving the eigenvalue problem of large N x N Hermitian matrices by using second-order recursion formulae is given. In principle, the method is suitable for finding not only the extreme eigenvalues and the corresponding eigenvectors but also any other eigenvalues in the range of one's specification. The effectiveness of the algorithm is illustrated by calculation of a few low-lying eigenvalues of the Heisenberg model for an antiferromagnetic chain with N up to 1048576.

Original languageEnglish
Pages (from-to)217-231
Number of pages15
JournalComputer Physics Communications
Volume96
Issue number2-3
Publication statusPublished - 1996 Aug 1

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Keywords

  • Eigenvalue problem
  • Hermitian matrices
  • Lanczos method
  • Large matrices
  • Schrödinger equations
  • Sparse matrices

ASJC Scopus subject areas

  • Hardware and Architecture
  • Physics and Astronomy(all)

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