### 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 |
---|---|

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 |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Computer Science Applications
- Physics and Astronomy(all)

### Cite this

*Computer Physics Communications*,

*96*(2-3), 217-231.

**A method for calculating the eigenvalues of large hermitian matrices by second-order recursion formulae.** / Mitsutake, Ayori; Iitaka, Toshiaki; Okamoto, Yuko.

Research output: Contribution to journal › Article

*Computer Physics Communications*, vol. 96, no. 2-3, pp. 217-231.

}

TY - JOUR

T1 - A method for calculating the eigenvalues of large hermitian matrices by second-order recursion formulae

AU - Mitsutake, Ayori

AU - Iitaka, Toshiaki

AU - Okamoto, Yuko

PY - 1996/8/1

Y1 - 1996/8/1

N2 - 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.

AB - 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.

KW - Eigenvalue problem

KW - Hermitian matrices

KW - Lanczos method

KW - Large matrices

KW - Schrödinger equations

KW - Sparse matrices

UR - http://www.scopus.com/inward/record.url?scp=0030213781&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030213781&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0030213781

VL - 96

SP - 217

EP - 231

JO - Computer Physics Communications

JF - Computer Physics Communications

SN - 0010-4655

IS - 2-3

ER -