Computing top eigenpairs of Hermitizable matrix

doi:10.1007/s11464-021-0909-6

Front. Math. China

2021, Vol. 16

Issue (2) : 345-379 https://doi.org/10.1007/s11464-021-0909-6

RESEARCH ARTICLE

Computing top eigenpairs of Hermitizable matrix

Mu-Fa CHEN^1,^2,³(

), Zhi-Gang JIA^1,⁴, Hong-Kui PANG^1,⁴

¹. Research Institute of Mathematical Science, Jiangsu Normal University, Xuzhou 221116, China
². School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
³. Laboratory of Mathematics and Complex Systems (Beijing Normal University), Ministry of Education, Beijing 100875, China
⁴. School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, China

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Abstract

The top eigenpairs at the title mean the maximal, the submaximal, or a few of the subsequent eigenpairs of an Hermitizable matrix. Restricting on top ones is to handle with the matrices having large scale, for which only little is known up to now. This is different from some mature algorithms, that are clearly limited only to medium-sized matrix for calculating full spectrum. It is hoped that a combination of this paper with the earlier works, to be seen soon, may provide some effective algorithms for computing the spectrum in practice, especially for matrix mechanics.

Keywords Hermitizable Householder transformation birth-death matrix isospectral matrices top eigenpairs algorithm

Corresponding Author(s): Mu-Fa CHEN

Issue Date: 01 June 2021

Cite this article:

Mu-Fa CHEN,Zhi-Gang JIA,Hong-Kui PANG. Computing top eigenpairs of Hermitizable matrix[J]. Front. Math. China, 2021, 16(2): 345-379.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-021-0909-6
https://academic.hep.com.cn/fmc/EN/Y2021/V16/I2/345

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