Efficient initials for computing maximal eigenpair

doi:10.1007/s11464-016-0573-4

Front. Math. China

2016, Vol. 11

Issue (6) : 1379-1418 https://doi.org/10.1007/s11464-016-0573-4

RESEARCH ARTICLE

Efficient initials for computing maximal eigenpair

Mu-Fa CHEN(

)

School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems (Beijing Normal University), Ministry of Education, Beijing 100875, China

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Abstract

This paper introduces some efficient initials for a well-known algorithm (an inverse iteration) for computing the maximal eigenpair of a class of real matrices. The initials not only avoid the collapse of the algorithm but are also unexpectedly efficient. The initials presented here are based on our analytic estimates of the maximal eigenvalue and a mimic of its eigenvector for many years of accumulation in the study of stochastic stability speed. In parallel, the same problem for computing the next to the maximal eigenpair is also studied.

Keywords Perron-Frobenius theorem power iteration Rayleigh quotient iteration efficient initial tridiagonal matrix Q-matrix

Corresponding Author(s): Mu-Fa CHEN

Issue Date: 18 October 2016

Cite this article:

Mu-Fa CHEN. Efficient initials for computing maximal eigenpair[J]. Front. Math. China, 2016, 11(6): 1379-1418.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-016-0573-4
https://academic.hep.com.cn/fmc/EN/Y2016/V11/I6/1379

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[1]	Mu-Fa CHEN, Yue-Shuang LI. Improved global algorithms for maximal eigenpair[J]. Front. Math. China, 2019, 14(6): 1077-1116.
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