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

Ayori Mitsutake; Toshiaki Iitaka; Yuko Okamoto

doi:10.1016/0010-4655(96)00067-7

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

Ayori Mitsutake, Toshiaki Iitaka, Yuko Okamoto

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	217-231
Number of pages	15
Journal	Computer Physics Communications
Volume	96
Issue number	2-3
DOIs	https://doi.org/10.1016/0010-4655(96)00067-7
Publication status	Published - 1996 Aug 1
Externally published	Yes

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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10.1016/0010-4655(96)00067-7

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

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.",

keywords = "Eigenvalue problem, Hermitian matrices, Lanczos method, Large matrices, Schr{\"o}dinger equations, Sparse matrices",

author = "Ayori Mitsutake and Toshiaki Iitaka and Yuko Okamoto",

note = "Funding Information: Our computations were performed on NEC SX-3/34R at the Institute for Molecular Science, Okazaki, Japan. This work was supported, in part, by the Collaboration Program of IMS and by the Special Postdoctoral Researchers Program of RIKEN.",

year = "1996",

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doi = "10.1016/0010-4655(96)00067-7",

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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

N1 - Funding Information: Our computations were performed on NEC SX-3/34R at the Institute for Molecular Science, Okazaki, Japan. This work was supported, in part, by the Collaboration Program of IMS and by the Special Postdoctoral Researchers Program of RIKEN.

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

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DO - 10.1016/0010-4655(96)00067-7

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SN - 0010-4655

VL - 96

SP - 217

EP - 231

JO - Computer Physics Communications

JF - Computer Physics Communications

IS - 2-3

ER -

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

Abstract

Keywords

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