### 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 language | English |
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Pages (from-to) | 217-231 |

Number of pages | 15 |

Journal | Computer Physics Communications |

Volume | 96 |

Issue number | 2-3 |

Publication status | Published - 1996 Aug 1 |

### 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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## Cite this

Mitsutake, A., Iitaka, T., & Okamoto, Y. (1996). A method for calculating the eigenvalues of large hermitian matrices by second-order recursion formulae.

*Computer Physics Communications*,*96*(2-3), 217-231.